a force-sensing device for assistance in soft-tissue
balancing during knee arthroplasty
THÈSE NO 3398 (2005)
PRÉSENTÉE à LA FACULTÉ SCIENCES ET TECHNIQUES DE L'INGéNIEUR
Institut de production et robotique
SECTION DE MICROTECHNIQUE
ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE
POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES
PAR
Denis CROTTET
ingénieur physicien diplômé EPF
de nationalité suisse et originaire de Portalban (FR)
acceptée sur proposition du jury:
Prof. H. Bleuler, directeur de thèse
Dr L. Dürselen, rapporteur
Prof. L. Nolte, rapporteur
Prof. P. Ryser, rapporteur
Lausanne, EPFL
2005
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“If you cannot measure it, you cannot improve it.”
Lord William Thomson Kelvin (1824-1907)
Acknowledgements
I would like to thank first Prof. Hannes Bleuler and Prof. Lutz-P. Nolte,
my supervisors, who gave me the opportunity to realize this interesting work
and who guided me throughout my doctoral thesis. My very warm thanks
also go to my co-advisers, Dr. Ion P. Pappas and Dr. Jens Kowal, for their
continuous support and their ideas, as well as their enthusiasm, which largely
contributed to the achievements presented herein.
For the helpful advice during the design phase and for the deposition of the
sensors, I am very grateful to Dr. Thomas Maeder and his team members,
Giancarlo Corradini, Caroline Jacq and Matthias Garcin, from the Laboratoire de Production Microtechnique, EPFL.
I heartily thank Dr. Sven Sarfert from the Department of Orthopaedic
Surgery of the Inselspital, Bern, for his clinical support during the in-vitro
studies and in-vivo trials. I particularly appreciated his availability, a rare
quality by surgeons.
I also thank very much Dr. Lutz Dürselen from the Institute of Orthopaedic
Research and Biomechanics, University of Ulm, Germany, for his collaboration and support during the in-vitro study.
My thanks go of course to all my colleagues who contributed to add to the
professional experience a unique human experience. The large variety of origins represented at the institute allowed me to discover different cultures and
wonderful people. Among these, I would like to address special thanks to the
so-called "French Connection" (even if a minority of members were French),
Heinz Waelti, Ségolène Tarte, Gisèle Douta, Serge Sagbo, Viton Vitanis, for
their friendliness, for the funny lunch breaks, for the moral support and for
all the nice souvenirs. To the technicians, Philippe Gédet, Thomas Beutler,
Ladina Ettinger and to the machine shop team, Urs Rohrer, Erland Mühleim,
Thomas Gerber, Remo Walther, Sebastian Marti, for their friendly, effective
III
IV
and high-quality assistance in producing mechanical parts, setting up experimental benches or testing materials. To Manuela Kunz, for her helpful
advice and ideas. To Anne Polikeit and Philippe Büchler for their technical
support in numerical simulations. To Haydar Talib and Paul Thistlethwaite,
who accepted the tedious task of proof reading the present thesis. To the
two sweetest secretaries (in literal and figurative meanings), Esther Gnahoré and Annelies Neuenschawander, for their good mood and their boosting
chocolates. And finally, to my former and current group colleagues, Jonas
Chapuis, Christian Sigrist, Jubei Liu, Puja Malik, Blake Borgeson, Elena
De Momi, Jaime Garcia, Brenton Ebert, Mario Löffel, Michaël Bläuer, Lars
Ebert, Marc Puls, Tobias Rudolph, Anna Martina Bröhan, who did their
best to transform the routine into a funny daily life.
Finally I am very grateful to all those,
accompanied me along these four years:
more particularly my wife Martine who
comforting words in the critical moments
in times of success.
outside the working sphere, who
my close friends, my family, and
always encouraged me by finding
and by lovingly congratulating me
Contents
Abstract
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Version abrégée
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1 Introduction
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2 Total knee arthroplasty
2.1 Anatomy of the knee . . . . . .
2.2 Total knee arthroplasty . . . . .
2.3 Computer assisted knee surgery
2.4 A force-sensing device for TKA
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3 Force-sensing device design
3.1 Simplified biomechanical model . . . . . . .
3.2 Techniques to measure forces . . . . . . . . .
3.2.1 Capacitive sensors . . . . . . . . . .
3.2.2 Magnetic, inductive sensors . . . . .
3.2.3 Strain gauges . . . . . . . . . . . . .
3.2.4 Choice of the measurement principle
3.3 Definition, evaluation of possible designs . .
3.3.1 Design I: opposed bending beams . .
3.3.2 Design II: open load cell . . . . . . .
3.3.3 Design III: integrated bridges . . . .
4 Thick-film piezoresistive sensors
4.1 Piezoresistive effect . . . . . . . . .
4.2 Thick-film technology . . . . . . . .
4.3 Mechanical properties . . . . . . . .
4.4 Custom low-temperature dielectric
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CONTENTS
VI
5 Calibration and intrinsic accuracy
5.1 Calibration method . . . . . . . . . . .
5.2 Intrinsic accuracy . . . . . . . . . . . .
5.3 Accuracy in the extended sensitive area
5.4 Accuracy with spacers . . . . . . . . .
5.5 Calibration and autoclave sterilization
5.6 Plastic deformation . . . . . . . . . . .
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6 In-vitro study
6.1 Control experiment with a plastic model
6.2 In-vitro trials . . . . . . . . . . . . . . .
6.3 In-situ evaluation . . . . . . . . . . . . .
6.3.1 Method . . . . . . . . . . . . . .
6.3.2 Results . . . . . . . . . . . . . . .
6.3.3 Discussion . . . . . . . . . . . . .
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7 Clinical trials
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7.1 Safety requirements . . . . . . . . . . . . . . . . . . . . . . . . 79
7.2 Standard approach vs force-sensing device . . . . . . . . . . . 82
8 Unicompartmental knee arthroplasty
8.1 Surgical procedure . . . . . . . . . . . .
8.2 Soft-tissue balancing assistance for UKA
8.2.1 Concept . . . . . . . . . . . . . .
8.2.2 In-vitro feasibility study . . . . .
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9 Conclusion and perspectives
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A Some basics of solid mechanics
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A.1 Elastic deformation . . . . . . . . . . . . . . . . . . . . . . . . 95
A.2 Stresses in beams . . . . . . . . . . . . . . . . . . . . . . . . . 99
B Contact pressure and stresses
B.1 Hertzian theory . . . . . . . . . . . . . . . . . . . . . . . . .
B.2 Distortion-energy criterion . . . . . . . . . . . . . . . . . . .
B.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Bibliography
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Curriculum Vitae
119
Abstract
Nowadays, the large majority of the instrumentation for orthopaedic surgery
consists of mechanical tools with varying degrees of complexity. To increase
the accuracy and the safety of orthopaedic interventions, sensors and computers were recently introduced in the operating room. Computer Assisted
Orthopaedic Surgery (CAOS) uses a navigation system that tracks the movements of surgical instruments in real-time and displays their exact location
in relation to the operative area. Such technology improved the quality of
orthopaedic arthroplasties, but it is still limited to the measurement of kinematic parameters such as axial alignments, position and angle measurements.
In Total Knee Arthroplasty (TKA), the ligament balance, which is crucial for
the stability and lifetime of implants, is currently only qualitatively assessed.
The goal of this thesis was therefore to demonstrate the importance of intraoperative measurement of musculoskeletal forces through the development of
a force-sensing device designed to improve the ligament balancing procedure
during TKA.
Three possible device designs were proposed and evaluated using finite element analysis in an iterative optimization process. The final design consists
of two sensitive plates, one for each condyle, a tibial base plate and a set of
spacers to adapt the device thickness to the patient-specific tibiofemoral gaps.
Each sensitive plate is equipped with three deformable bridges instrumented
with thick-film piezoresistive sensors, which allow accurate measurements of
the amplitude and location of the tibiofemoral contact forces. The net varusvalgus moment is then computed to characterize the ligament imbalance.
Laboratory experiments showed that the device has appropriate accuracy
and dynamic range for the intended application. The first experimental trials on a plastic knee joint model and on a cadaver specimen demonstrated
the proper in-situ functioning of the device. The performance and surgical
advantages of the device were then evaluated in an in-vitro study including
four different experiments: 1) Six knee joints were axially loaded. Com1
2
ABSTRACT
paring applied and measured compressive forces demonstrated the accuracy
and reliability of in-situ measurements. 2) To estimate the importance of
keeping the patella in its anatomical place during imbalance assessment, the
effect of patellar eversion on the mediolateral distribution of tibiofemoral
contact forces was measured. One fourth of the patellar load was shifted to
the lateral compartment. 3) Assessment of knee stability based on condyle
contact forces or varus-valgus moments were compared to the current surgical method (difference of varus-valgus loads causing condyle lift-off). The
force-based assessment found to be equivalent to the surgical method while
the moment-based technique, which is considered optimal, showed a tendency of lateral imbalance. 4) Finally the effect of minor and major medial
collateral ligament releases was biomechanically quantified. Large variation
among specimens reflected the difficulty of ligament release and the need for
intraoperative force monitoring.
Two clinical trials were carried out to evaluate the device performance in a
surgical environment. After the tibial cut, the medial and lateral tibiofemoral
gaps ensuring the knee stability were determined from the device measurements and compared to the femoral cuts performed on the basis of standard
instrumentation. The agreement between the two approaches was generally
good. The only significant difference was measured on the first patient at
90◦ flexion. At this point, the surgeon also estimated that the knee was not
optimally balanced, thus demonstrating the consistency between his perception and the device measurements.
In conclusion, the proposed force-sensing device for assistance in ligament
balancing during TKA provides accurate, reliable and useful measurements.
In addition to the precise imbalance assessment based on the measurement
of forces and moments, important clinical advantages, such as the possibility to keep the patella in its anatomical place during the measurement or
the real-time force monitoring during the delicate phase of ligament release,
were demonstrated. The encouraging results of the in-vivo trial proved the
usability of the device in a surgical environment and opens the way for larger
clinical studies. The developed device has thus potential to improve the
ligament balancing procedure, the consistency of surgery and the lifetime
of TKA, illustrating thereby the clinical benefit of measuring forces during
orthopaedic surgeries.
Version abrégée
De nos jours, la majeure partie de l’instrumentation pour la chirurgie orthopédique est constituée d’outils mécaniques plus ou moins complexes. Afin
d’améliorer la précision et la sécurité de ces interventions, senseurs et ordinateurs ont récemment fait leur apparition en salle d’opération. La chirurgie
orthopédique assistée par ordinateur utilise un système de navigation qui
suit en temps réel les mouvements des instruments chirurgicaux et affiche
leur position exacte par rapport à la zone opérée. Une telle technologie a
amélioré la qualité des interventions mais reste malheureusement limitée à la
mesure de paramètres cinématiques tels que axes, angles ou positions. Lors
d’Arthroplastie Totale du Genou (ATG), l’équilibre ligamentaire, qui est crucial pour la stabilité et la durée de vie des implants, est actuellement évalué
uniquement qualitativement à l’aide de manipulations ou d’outils basiques.
Le but de cette thèse était donc de montrer l’importance de la mesure intraopératoire des forces musculosquelettiques au travers du développement
d’un capteur de force conçu pour améliorer la procédure d’équilibrage ligamentaire lors d’ATG.
Trois designs possibles ont été proposés et évalués en utilisant la méthode
des éléments finis au cours d’un processus itératif d’optimisation. Le design final comprend deux plaques sensibles, une pour chaque condyle, une
plaque de base tibiale et un set d’écarteurs pour adapter l’épaisseur du capteur à l’espace tibiofémoral du patient. Chaque plaque sensible comprend
trois ponts déformables équippés de senseurs piézorésistifs qui permettent
de mesurer précisément l’amplitude et la position des forces de contact des
condyles fémoraux. Le moment résultant dans les directions varus et valgus
est ensuite calculé pour caractériser l’équilibre ligamentaire.
Les expériences en laboratoire ont montré que le capteur a une précision et
une plage de mesure appropriées pour l’application envisagée. Les premiers
essais sur un modèle en plastique et sur un spécimen cadavérique ont démontré le bon fonctionnement du capteur in-situ. Les performances et les
3
4
VERSION ABRÉGÉE
avantages chirurgicaux du capteur ont ensuite été évalués au travers d’une
étude in-vitro comprenant quatre expériences différentes: 1) Six genoux ont
été chargés axialement. La comparaison entre les forces de compression appliquées et mesurées a démontré la précision et la fiabilité des mesures in-situ.
2) Afin d’estimer l’importance de garder la rotule à sa place anatomique
durant l’évaluation du déséquilibre, l’effet d’une éversion rotulienne sur la
distribution mediolatérale des forces de contact a été mesuré : un quart de la
force rotulienne est déplacé sur le compartiment latéral. 3) L’évaluation de la
stabilité du genou basée sur les forces de contact des condyles ou sur leur moment a été comparée à la méthode chirurgicale actuelle (différence de poids
varus ou valgus créant un décollement d’un condyle). L’évaluation basée
sur les forces fut équivalente à l’approche chirurgicale alors que celle basée
sur les moments, considérée comme optimale, a montré une tendance à un
déséquilibre latéral. 4) Finalement, l’effet de relâches ligamentaires mineures
ou majeures du ligament collatéral médial a été quantifié biomécaniquement.
L’importante variation parmi les spécimens a révélé la difficulté de la relâche
ligamentaire et le besoin d’un monitoring intraopératoire des forces.
Deux essais cliniques ont été effectués pour évaluer le fonctionnement du
capteur dans un environnement chirurgical. Après la coupe tibiale, les espaces tibiofémoraux médial et latéral assurant la stabilité du genou ont été
déterminés selon les mesures du capteur et comparés aux coupes fémorales effectuées sur la base de l’instrumentation habituelle. L’accord entre les deux
approches était généralement bon. La seule différence significative a été
mesurée sur le premier patient à 90◦ de flexion. A ce moment, le chirurgien
estimait également que le genou n’était pas équilibré de façon optimale, démontrant ainsi la cohérence entre sa perception et les mesures du capteur.
En conclusion, le capteur de force proposé pour l’assistance durant l’équilibrage ligamentaire lors d’ATG fournit des mesures précises, fiables et utiles.
En plus d’une évaluation quantitative du déséquilibre basée sur la mesure de
forces et de moments, des avantages cliniques importants ont été démontrés,
comme par exemple la possibilité de garder la rotule à sa place anatomique
ou le monitoring des forces de contact lors de la relâche ligamentaire. Les
résultats encourageant de l’essai clinique ont prouvé que le capteur fonctionne
parfaitement dans un environnement chirurgical, ouvrant ainsi la voie à de
plus larges études cliniques. Le capteur développé a donc montré un potentiel
pour améliorer la procédure d’équilibrage ligamentaire, la consistance de la
chirurgie et la durée de vie d’une ATG, illustrant ainsi le bénéfice de mesures
de forces lors d’opérations orthopédiques.
Chapter 1
Introduction
Orthopaedic surgery, which is the branch of surgery concerned with injuries
and disorders of the musculoskeletal system, is an ancient discipline. Archeological traces, such as a prosthesis for a big toe after a healed amputation
found on a mummy (circa 1065-650 BC) [1] or the guidelines and reports
of surgical cases in the Edwin Smith papyrus (circa 1700 BC) [2], were discovered in Egypt. Other ancient civilizations, such as Greeks or Romans,
reported orthopaedic knowledge as well. Various volumes of the important
Greek text Corpus Hippocrates (circa 430-330 BC) from the name of the
famous father of medicine had relevance to orthopaedics. For example, an
entire volume is dedicated to joints, where dislocation of the shoulder, knee,
hip and elbow joint was described together with the various methods used
for reduction. It was nevertheless not before the l2th century that Europe
began to awake gradually from its dark ages. Universities and hospitals were
being established, human dissection resumed and the great Greek texts were
being translated. However, until the l6th century, all developments remained
within the shadow cast by Hippocrates. Some of the new techniques introduced at that time were the use of a tourniquet and the ligature for large
vessels for amputations or the development of artificial limbs using iron or
wood. Modern orthopaedics started only in the early 1900’s with the discovery of the X-ray and with the fact that orthopaedics became a specialty in
its own. From that point in time the tools for diagnosis, surgical techniques
and instrumentation had been continuously improved to the end of obtaining
predictable and satisfying outcome of orthopaedic interventions.
Nowadays, the large majority of the instrumentation for orthopaedic surgery
consists in more or less complex mechanical tools. Chisels, saws, drillers
required to correct or repair bony structure are used in combination with
mechanical ancillaries, providing the surgeon with geometrical parameters
5
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CHAPTER 1. INTRODUCTION
such as bone axes, morphologic angulations or distances between bones. To
increase the accuracy and the safety of orthopaedic interventions, sensors
and computers were recently introduced in the operating room. Computer
Assisted Orthopaedic Surgery (CAOS) uses a navigation system that tracks
in real-time the movements of the surgical instruments and displays their
exact location in relation to the operative area [3]. Such technology enables
more precise placement of implants and safer delicate surgical actions, such
as the insertion of a pedicle screw in a vertebral body. With the arrival
of CAOS systems, surgical instrumentation reached an important turning
point and is now experiencing the same natural evolution as the automotive
industry during these past decades. Sensors, calculators, automatic control
or management are common features in cars nowadays. An Audi A8 for instance contains 45 calculators in its standard version and more than 75 with
full options. Even though refractories claimed that this proliferation of electronic components in cars would just increase the risk of break-downs, a large
number of new technologies such as airbags, Anti-lock Brake System (ABS),
automatic gear change or power-assisted steering have significantly improved
the safety and comfort of the end users. According to the first short-term
clinical studies, the same benefits can be hoped in the CAOS systems.
However, current navigation systems, although competitive, are mainly limited to the control of geometrical parameters. Stresses in soft-tissue or forces
applied by the surgeon are important biomechanical parameters which usually remain unknown. Measurement of forces with smart instrumentation
can therefore improve the quality of orthopaedic surgery in three different
ways:
1. Detection of possible damage of healthy tissues. When the surgeon
has no direct access to the operation site, as during minimally invasive surgery, manual guidance of the tools is difficult. Integrating force
sensors in the surgical tools can help to detect undesired contact or
penetration in healthy tissue. For example, an arthroscope equipped
with force sensors can detect contact between its tip and the surrounding tissues [4], thus preventing possible damage of the cartilage. A
second example of application is a mechatronic tool for drilling in the
osteosynthesis of long bones [5]. In that case, the measurement of the
variation of the thrust force experienced by the driller allows determining if the drill bit is in cancellous or cortical bone. When a bone is
drilled across, the time of incipient breakthrough on the second cortical wall can thus be detected and the hole completed with minimal
protrusion of the drill bit from the bone.
7
2. Force monitoring of surgical actions. While being corrected, cut, rasped,
or reshaped, bones experience relatively high stresses. Applying excessive forces on the bony structure can create irreversible damage or give
suboptimal outcomes. Instrumenting orthopaedic tools with force sensors can provide useful real-time force-feedback and thereby ensure safe
and optimal surgical actions. In the case of correction of scoliosis for
example, the realignment of the spine is realized by implanting a rod
screwed in the misaligned vertebral bodies. In addition to the axial
pull-out strength, the screws are loaded with a force component perpendicular to the screw axis, which may weaken the bone around the
head and lower the pull-out force. A high correction force therefore
increases the risk of screw pull-out. Instrumented forceps that measure
tensile forces in the different segment of the rod can thus be used to
maintain constant axial forces in the rod and reduce the transverse force
on the vertebral screws [6]. A second example of application could be
rasps instrumented with force sensors for the preparation of the femoral
cavity in hip arthroplasty. Since there is a direct correlation between
the rasping force and the bone density, the measurement of the latter
allows the determination of the optimal rasping force. This optimum
can then be intraoperatively guaranteed thanks to a monitoring based
on the smart rasp measurements, thus avoiding excessive forces that
may damage the femur.
3. Assistance for optimal adjustment of the soft-tissue forces in joint arthroplasty. Joint arthroplasty is used to treat severe arthrosis and bone
deformities. To achieve a satisfying stability and lifetime of the prosthetic joint, the alignment of the bones and the forces experienced by
the surrounding soft-tissue must be optimally corrected at the time of
the surgery. The intraoperative use of instrumented trial implants or
specific force-sensing devices could provide valuable measurements to
assist the surgeon in optimally balancing the soft-tissue tensions. Two
different applications can be thought for the two most performed joint
arthroplasties: an instrumented telescopic neck for Total Hip Arthroplasty (THA) and a force-sensing device for Total Knee Arthroplasty
(TKA). One serious problem after THA is dislocation, which is attributed to component malpositioning, soft-tissue imbalance and impingement. An advanced trial implant could allow the medialization
and lateralization of the prosthesis and the measurement of the resultant hip force by means of a telescopic neck instrumented with forcesensors. The surrounding soft-tissue such as muscles, fascia, could be
more or less stressed by adjusting the length of the neck until the op-
8
CHAPTER 1. INTRODUCTION
timal resultant hip force is obtained. This procedure may then lead to
the proper choice of the prosthetic components, reducing the rate of
dislocations in THA. In the knee, the stability of the joint is realized by
a complex ligament structure. At the time of arthroplasty, this stability
must be reevaluated and, if necessary, corrected to ensure a successful
outcome. A force-sensing device that can precisely measure intraoperative mediolateral imbalance of the compressive forces of the knee
joint could assist the surgeon in this delicate phase of ligament balancing. This would guarantee an optimal distribution of the compressive
forces,leading to an increased lifetime of the prosthetic implants.
The goal of the present work is therefore to demonstrate through an application the importance and benefit of advanced orthopaedic instrumentation
providing quantitative knowledge of intraoperative forces. A force-sensing
device for improved ligament balancing procedure in knee arthroplasty has
been developed and tested. Chapter 2 presents general aspects of the knee
joint anatomy and of TKA as well as the specifications of such force-sensing
device. The different conceived designs are explained and studied in chapter
3, while the selected sensor technology is described in chapter 4. The calibration method and the evaluation of the intrinsic accuracy of the device
is exposed in chapter 5. The result of the in-situ evaluation of the device
design as well as biomechanical investigations about the effect of ligament
releasing can be found in chapter 6. Finally, the possible extension of the developed device to unicompartmental knee arthroplasty is discussed in chapter
8, before concluding this thesis in chapter 9.
Chapter 2
Total knee arthroplasty
2.1
Anatomy of the knee
The knee is the largest and most complex joint in the human body and combines two major joint mechanisms. On one hand, it fulfills the requirements
of stability, which allows the transmission of large forces. For example, the
knee bears three to four times the body weight during stair climbing. On
the other hand, it provides a high degree of flexibility with a range of motion of up to 140◦ in flexion. The combination of these two functionalities
is only possible by a perfect interplay between all the components of the knee.
The knee is indeed a two-joint structure composed of the tibiofemoral and
patellofemoral joints [7]. The tibiofemoral joint connects the two longest
bones in the human body, namely the femur and the tibia (Fig.2.1). The
joint-constructing bone segments are overlaid by cartilage, which protects
the bones and ensures free sliding. The absence of bony guidance is compensated by a complex structure of ligaments, which are dense parallel-fibered
collagenous tissue. Two collateral ligaments (medial and lateral) limit the
mediolateral translation from the tibia with respect to the femur and the
so-called abduction-adduction rotation movements. Two cruciate ligaments
(anterior and posterior) restrict the translation of the tibia to the femur in
anterior and posterior directions. In the tibiofemoral gap are found the lateral and medial menisci, which compensate the bony incongruency and allow
compressive forces to be distributed over the entire area of the tibial plateau,
thus minimizing the contact stresses.
The patellofemoral joint (Fig.2.2) consists of the femur and the patella, which
is a flat bone placed as a cap to the knee. The patella is held by the patellar
9
10
CHAPTER 2. TOTAL KNEE ARTHROPLASTY
Figure 2.1: Anatomy of the knee
(picture adapted from the anatomy atlas of ADAM, Atlanta, USA)
tendon on the tibial side and by the quadriceps, the most effective active
knee stabilizers, on the femoral side. The patellofemoral joint supports the
extension of the knee and works as a sagittal stabilizer. The patella is also a
protection for the knee in the frontal plane.
Quadriceps
Patella
Patellar tendon
Figure 2.2: Patellofemoral joint
(picture adapted from the anatomy atlas of ADAM, Atlanta, USA)
All these components are the basis of the four degrees of freedom motion of
the knee (Fig.2.3). In addition to three rotations (flexion-extension, varusvalgus and rotation), the tibia can perform anterior-posterior translations.
2.2. TOTAL KNEE ARTHROPLASTY
11
This results in a complex relative motion between the tibia and femur during
a gait cycle: the flexion of the knee is accompanied by an external rotation and a posterior sliding of the femur [8]. A detailed description of knee
kinematics can be found in [9].
Figure 2.3: Possible motions of the knee
2.2
Total knee arthroplasty
Total Knee Arthroplasty (TKA) is the surgical intervention which consists
of replacing a painful, damaged or diseased knee joint with prosthetic components. TKA is usually indicated for patients with end-stage degenerative
disease, such as osteoarthrosis.
Even though T. Gluck designed and implanted hinge knee prostheses made of
ivory over 100 years ago [11], intensive development of TKA had started by
the 1950s. Design limitations in those early days included improper sizing,
no provision for replacing the patellofemoral joint, lack of rotational freedom
and improper stem fixation. Design of condylar knee replacement and polycentric knees were developed by the 1970s, while the 1980s and 1990s were
spent for design improvements, thus allowing: better fixation with or without
cement; reduced wear; enhanced kinematics and increased range of motion.
The standard modern artificial joint is composed of three parts: metallic
femoral and tibial components, which replace the bony structures, and a
polyethylene inlay, which plays the role of the removed menisci (Fig.2.4).
In the current age of technological advances, reproducing knee kinematics,
12
CHAPTER 2. TOTAL KNEE ARTHROPLASTY
minimizing wear and increasing range of motion beyond 125◦ with proper
alignment and stability have become the major goals of TKA [12].
Figure 2.4: Total Knee Arthroplasty
Artificial knee joints are comprised of metallic femoral and tibial components and an
inlay that plays the role of the removed menisci. (components picture taken from
Zimmer, Warsaw, USA and drawings from Plus Orthopaedics, San Diego, USA)
To obtain a successful TKA, it is essential to produce a neutral mechanical
axis from the center of the femoral head through the center of the knee to the
center of the ankle by creating a valgus anatomic alignment of the femoral
and tibial axes. If the limb alignment is suboptimal, the distribution of the
load created by the body weight is not homogeneously distributed and may
provoke postoperative complications such as component loosening or fast implant wear. The classic alignment involves the resection of the proximal tibia
at a right angle to the long axis of the tibia from an anterior view. This
is in contrast to the normal alignment of the articular surface which lies
at approximately 4 ◦ of varus with respect to the tibia’s anatomic axis [13]
(Fig.2.5). Consequently, more bone is removed from the lateral tibial plateau
than from the medial plateau. Accordingly, a larger amount of bone would
be resected on the medial posterior femoral condyle than on the lateral in
order to create a symmetric, rectangular flexion space, which is essential for
proper collateral ligament function. This rotational positioning concept has
become known as "external rotation of the femoral component".
In addition to a good tibiofemoral alignment, the stability of the knee joint
must be ensured. This involves balancing the medial and lateral ligamentous
structures. Medial ligament releases are indicated in a knee arthroplasty in
which the patient has varus misalignment, which is the deformity that sur-
2.2. TOTAL KNEE ARTHROPLASTY
13
Figure 2.5: Classic bone resection during TKA
(picture taken from [16])
geons encounter most frequently. In case of a valgus knee — rarer but which
presents more challenges to the surgeon — the tightest lateral structure is
released. Diverse techniques to release ligaments have been reported [14, 15].
Although the approaches can differ among surgeons, a release consists in a
partial resection of the fibers constituting the ligament. By doing so, the
ligament stiffness is diminished and the tension reduced. This surgical action is of course irreversible and can be used only to reduce tension of tight
structures.
Other important concerns in TKA are the preservation of the joint line, the
contact line between the tibia and the femur, and the minimization of bone
removal. Elevation of the joint line from its anatomic position alters normal
ligament function whereas excessive bone resection reduces the stability and
limits the chance of a successful revision at a later stage.
At the end of the surgery, i.e. following the bone cuts and the insertion of
trial components, the final knee stability is evaluated in flexion and extension.
In full extension, three criteria must be met (Fig.2.6):
1. Absolutely full extension without recurvatum or residual flexion contracture
2. Satisfactory valgus anatomic alignment (neutral mechanical axis)
3. Satisfactory varus-valgus stability.
14
CHAPTER 2. TOTAL KNEE ARTHROPLASTY
In flexion the knee should feel just slightly more lax than in extension [16].
Figure 2.6: Evaluation of the knee in extension with trial components
A: The knee should achieve full extension without recurvatum B: The mechanical axis
should be neutral C: Satisfactory varus-valgus stability (picture taken from [16])
To resume, the key points to reach a successful primary knee arthroplasty
are establishment of correct mechanical alignment, maintenance of joint stability, preservation of joint line and minimal bone resection [17]. Nevertheless recent analysis showed that failure rates of primary TKA are 9% at 10
years, 16% at 15 years and 22% at 20 years [18]. Common causes of dysfunction after TKA are component loosening and instability. It is nowadays
widely accepted that the two surgical factors responsible for these postoperative complications are tibiofemoral misalignment and ligament imbalance
[19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. In order to increase the long term success rate of TKA, advanced instrumentation allowing optimal limb alignment
and accurate ligament balance must be placed at surgeons’ disposal.
2.3. COMPUTER ASSISTED KNEE SURGERY
2.3
15
Computer assisted knee surgery
Although the concept of navigating a surgery is over 100 years old, the intensive development of Computer Aided Orthopaedic Surgery (CAOS) started
in the early 1990s. Like every surgical navigation system, CAOS consists
of three major components: the therapeutic object (the patient), the virtual object (computed tomography, fluoroscopic images or digitized points
or curves) and a navigator, a device which links the therapeutic object and
the virtual object [29]. Thanks to this navigator, the surgeon always knows
the exact location of the tools in the virtual object. Before each crucial step,
he can precisely check that the location and orientation of his tool is correct
according to his planning and is therefore able to safely and precisely drill or
saw the bones.
For example, current surgical knee navigation systems help the surgeon
achieve a precise alignment and placement of the prosthetic components. Following the registration of the knee anatomy, the navigation system proposes
optimal cuts and component size in order to obtain a neutral mechanical
axis of the limb. Postoperative knee kinematics can also be simulated at the
time of surgery in order to anticipate what the future range of motion will be
and, if necessary, to perform final adjustments. The clinical benefit of such
technology has nowadays been extensively reported [30, 31, 32, 33, 34].
Even though good tibiofemoral alignment can be achieved with current CAOS
navigation systems, only geometric parameters such as morphologic angulation, depth penetration, etc., are provided. Ligament force imbalance during
TKA is still qualitatively assessed by the surgeon through manual trial movements of the limb. Providing an objective and quantitative measurement of
the forces acting within the knee could help the surgeon improve the accuracy of the ligament balancing procedure, leading to a potentially longer
prosthesis lifetime.
2.4
A force-sensing device for TKA
Various approaches to intraoperatively measure ligament imbalance were reported and are presented below.
Attfield et al. [35] developed an electronic surgical instrument which contains
two plates, one being attached to the tibia, the other supporting the femur.
The upper plate acts as a mechanical cantilever in the medial-lateral direc-
16
CHAPTER 2. TOTAL KNEE ARTHROPLASTY
tion and the ligaments are balanced according to the measured inclination
of the cantilever, which depends on the moments applied by the soft tissues.
The disadvantage of such an apparatus resides in the size of the handle that
prevents the patella from being kept at its anatomical place during the measurement. Undesirable forces are thus generated by the patella tendon and
may lead to a non-optimal balancing.
Wallace et al. [36] used a dual-array electronic pressure transducer (Tekscan,
Boston, United States). The 10% intrinsic accuracy of the device might be
insufficient for such an application and the large number of wires needed for
the pressure sensor arrays and the data acquisition requires an arthrotomy
through the patellar retinaculum. Similar sensing technology from Novel
Electronics, Munich, Germany, was recently used to determine the correlation of intraoperative pressure with postoperative knee kinematics [37, 38].
Knee joint pressure distribution was also measured intraoperatively with Fuji
pressure-sensitive films [39], but the accuracy is relatively low and the reading is not available in real-time.
In another development, an implantable tibial tray was instrumented with
four load cells and a passive telemetric transmission system [40, 41, 42]. In
addition to the long-term post-operative use, it is possible to intraoperatively
measure the contact forces of the femoral condyles. Nevertheless, in order
to accommodate the load cells, this customized tibial tray is 7.5mm thicker
than that of a standard prosthesis, which requires significantly larger bone
removal. Davy et al. [43] reported a similar development.
Different designs of calibrated pliers are commercially available for controlled
knee distraction. A tensor/balancer device (Stryker Howmedica Osteotonics,
Mahwah, United States) was evaluated in 83 consecutive TKAs by Winemaker, who concluded that the device provides an accurate and reproducible
way to measure gap differences and angular asymmetry [44]. The BalanSys
knee instrument (Mathys LTD Bettlach, Bettlach, Switzerland) is a similar
device composed of two calibrated spring tensors that allow medial and lateral
force-controlled gap distraction. Finally, an instrumented ligament spreader
was combined with the Galileo knee replacement navigation system (PiSystems, Aarau, Switzerland), thus providing a tension/force and a distance
measurement as well as information regarding the polyethylene thickness to
be selected [45]. Even though the approach is simple and appears efficient,
all these devices are encumbering and requires a patellar eversion or subluxation, which can again significantly alter the ligament balance.
2.4. A FORCE-SENSING DEVICE FOR TKA
17
Marmignon et al. [46] developed a robotized distraction device, which has
a base plate carrying two independent and parallel trays. These trays that
support the condyles can be elevated thanks to a jack and a cable applying a
force between the central axes or due to two inflatable rubber bladders. The
first approach lead to a device not powerful enough (100N maximal force),
while in the second, the parallelism of the trays could not be ensured, thus
preventing the proper functioning of the device.
To overcome these disadvantages, the optimal force-sensing device for TKA
must fulfill the following requirements:
1. Accurate and real-time quantitative measurements to optimally balance
the ligament forces
2. Minimal thickness and easy insertion to minimize the tibial resection
and avoid any additional surgical actions
3. Adaptable thickness to allow the correction of the tibiofemoral alignment and the compensation for the anatomic variation of each patient
4. Measurements with the patella in its anatomical place to avoid nonanatomical forces due to a patellar eversion or subluxation.
5. Possibility to measure the ligament balance before the femoral cuts.
Performing the assessment of the joint stability at an early stage of
the TKA procedure offers the possibility to make a better plan for the
femoral cuts and the femoral component rotation. The joint line can
be more easily preserved and the bone resection minimized. Moreover,
strong imbalance that could not be corrected at a later stage with only
ligament releases could be rectified at the beginning of the surgery when
all the correction means, such as bone cuts, are still at the surgeon’s
disposal.
18
CHAPTER 2. TOTAL KNEE ARTHROPLASTY
Chapter 3
Force-sensing device design
Before designing the device, the biomechanical parameters that characterize
the ligament balance must be determined. For that purpose, a simplified
biomechanical model of the knee joint is first introduced. Since the design
depends as well on the type of sensors selected, several principles of force
measurement are then explained. Finally, three possible designs are presented
and evaluated using finite element analysis. Basic concepts of mechanics of
material necessary to understand the measurement principle of the different
designs are recalled in appendix A.
3.1
Simplified biomechanical model
To ensure a stable knee joint and therefore a successful outcome of TKA, it
is assumed that the ligament forces must be balanced (c.f. chapter 2). In order to define the relevant parameters characterizing this balance, a simplified
model of the knee joint in the coronal plane is used. It considers the collateral ligament forces FM L , FLL and the condyle contact forces acting on the
tibia FM C , FLC (Fig.3.1). The cruciate ligaments and the patella tendon are
neglected since their effect is mainly limited to the sagittal plane. Although
quite simple, this model captures the most important knee balance effects in
the coronal plane.
In static conditions, the mechanic equilibrium equations (
0 ) must be satisfied, yielding:
i Fi = 0,
i Mi =
0 = FM L + FLL − FM C − FLC
0 = xM L FM L − xLL FLL − xM C FM C + xLC FLC
(3.1)
where xi (i = M L, LL, M C, LC) are the lever arms of the different forces
measured from the origin placed at L/2, L being the distance between the
19
20
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
FML
FLL
FMC
FLC
z
y
x
Figure 3.1: Two-dimensional knee joint model
The patella tendon and the cruciate ligaments being mainly effective in the sagittal
plane, only the collateral ligament forces (FM L , FLL ) and the contact forces (FM C , FLC )
are taken into account.
collateral ligaments. The lever arms of the collateral ligaments being L/2,
equation (3.1) becomes:
Mnet = xM C FM C − xLC FLC =
L
(FM L − FLL )
2
(3.2)
where Mnet is the net varus-valgus moment of the contact forces acting
on the knee joint. When the tension in the collateral ligaments is equal
(FM L = FLL ), the right side of the equation is zero. Therefore, Mnet may
be regarded as the parameter characterizing the ligament imbalance, and
reducing it to zero is equivalent to balancing the ligaments. In conclusion,
the device must be able to either measure this net varus-valgus moment or
measure parameters that allow its computation.
3.2
Techniques to measure forces
As a force can not be measured directly, its effect on a body, such as the
resulting deformation or displacement, must be assessed. For example, the
strain experienced at the base of a bending beam is directly proportional to
3.2. TECHNIQUES TO MEASURE FORCES
21
the force applied at the beam extremity by the well-known flexure formula
(c.f. equation (A.22)). Four types of force sensors have been investigated for
our application: capacitive, magnetic, inductive sensors and strain gauges.
3.2.1
Capacitive sensors
A capacitor is schematically represented by two conductors separated by a
gap. Its capacitance is a function of the area S of the conductors and the
gap d:
S
(3.3)
C= ,
d
where is the dielectric constant of the gap. According to equation (3.3) a
gap change, which is a relative displacement of the conductors, leads to a
variation in the capacitance.
A capacitor connected to an inductor forms a resonant circuit (Fig.3.2). The
gain function of such circuit is given by:
Uo ZC 1/jωC
1
=
=
,
G(ω) = = Ui
ZC + ZL 1/jωC + jωL 1 − ω 2 LC where Ui , Uo are the input and output voltages, ω the pulsation and ZC ,
ZL the complex impedances of the capacitor and inductor respectively.
In
1
LC
view of this last expression, the gain amplitude is infinite when ω =
1
1
ν = 2π
, which is called the resonance frequency.
LC
G(w)
L
Ui
C
Uo
w
1
LC
Figure 3.2: LC resonant circuit
The LC circuit scheme and its corresponding Bode diagram
or
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
22
Capacitive sensors can therefore be placed in such a manner that the application of a force makes d or S, and thereby the capacitance C, vary. By
integrating the sensor in a resonant circuit, the applied force can be retrieved
by measuring the change of the resonance frequency.
3.2.2
Magnetic, inductive sensors
Another possibility to measure forces is to use magnetic or inductive sensors. In both cases, the measurement system is composed of an emitter and
a receiver. The emitter generates a magnetic field and is mounted on a part
of the sensing device which is deformed by the applied load. The receiver
is placed on a fixed reference part and measures the variation of the magnetic field induced by the emitter displacement. Since the emitter position
is dependent on the applied load, a direct relationship exists between the
magnetic field variation measured by the receiver and the applied load.
The measurement principle of the magnetic and inductive sensors is as follows:
1. Magnetic sensors
• The emitter is a permanent magnet.
• The receiver is a magnetic field detector based on the Hall effect
(Fig.3.3). When a electrical current traverses a metallic plate submerged in a magnetic field, the electrons going through the plate
experience a Lorentz force perpendicular to the current direction.
A measurable voltage, whose amplitude varies proportionally to
that of the magnetic field, appears at its border.
B
I
V=0
e-
V=VH
Figure 3.3: Illustration of the Hall effect
When an electrical current (I) traverses a metallic plate submerged in a magnetic field
(B), the electrons are deviated and a voltage (VH ) is generated at the borders.
3.2. TECHNIQUES TO MEASURE FORCES
23
2. Inductive sensors
• The emitter is a coil powered by an alternative current, thus generating an oscillating magnetic field.
• The receiver is a coil too, into which the emitted magnetic field
induces a current. The amplitude of the induced current varies
with the magnetic field amplitude.
3.2.3
Strain gauges
A strain gauge is a device whose electrical resistance varies in proportion to
the amount of strain in the device. The most widely used gauge is the bonded
metallic strain gauge. The metallic strain gauge consists of a fine wire or,
more commonly, metallic foil arranged in a grid pattern. The grid pattern
maximizes the amount of wire to strain in the direction parallel to the gauge
backing (Fig.3.4). The cross-sectional area of the grid is minimized to reduce
the effect of shear strain and Poisson strain (c.f. appendix A). The grid is
bonded to a thin backing, which is attached directly to the test specimen.
Therefore, the strain experienced by the test specimen is transferred directly
to the strain gauge, which responds with a linear change in electrical resistance due to the lengthening or shortening of the metallic foil.
Figure 3.4: Metallic strain gauge
A strain gauge is basically a thin wire arranged in a grid pattern whose resistance
linearly varies with the strain.
Although this low-cost technology gives a large freedom to the designer, a
few delicate points such as the bonding and the positioning have to be considered. It is very important that the strain gauge is properly mounted onto
the test specimen so that the strain is accurately transferred from the test
specimen, through the adhesive and strain gauge backing, to the foil itself.
Bad mounting not only affects the measurement sensitivity, but also causes
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
24
self-heating problems. Inaccurate positioning, such as bad parallelism, generates deviations by not measuring the desired force, but only its projection
on the gauge axis.
Piezoresistive sensors
To overcome the disadvantages of bonded metallic strain gauges, piezoresistive ceramic elements can be used instead (c.f. chapter 4). In addition
to a larger gauge factor, which is the ratio between the strain and resistance variation, and a larger resistance, which reduces the self-heating due
to the Joule effect, thick-film piezoresistive sensors can be directly deposited
on the specimen by screen printing. With such technology, errors due to
bad mounting are minimized. Furthermore, the size of piezoresistive sensors
are significantly reduced compared to that of standard strain gauges, thus
allowing finer designs.
3.2.4
Choice of the measurement principle
Although each of the previously discussed sensor types could be used, thickfilm piezoresistive sensors have been chosen for the following reasons:
• The measurement principle is relatively simple.
• The encumbrance is not significant.
• The intrinsic accuracy of the sensor is high.
• It is a low-cost technology.
• The signal conditioning can be ensured with just an amplifier and a
filter.
• Standard heat moisture sterilization is possible.
• Biocompatibility can be easily ensured by a final surface coating.
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
3.3
25
Definition, evaluation of possible designs
Before describing in details the three designs, the common aspects, such as
the perimeter, the different parts composing the device and the material selected are presented.
The three conceived designs were inspired from existing prosthetic components. The perimeter of the device was extracted from a CKS inlay (Biomet,
Warsaw, IN, USA). It is 77mm wide and 51mm long, so it is suitable for
tibias of medium size. In case of routine clinical use, the device would be
available in different scales to cover all the possible knee sizes.
A flat reference surface on the tibial side is required to ensure reliable measurements. Moreover, compressive forces or varus-valgus moments have to
be assessed with different knee gaps to comply with the surgical procedure.
For these reasons, the device is composed of three distinct parts:
1. A tibial base plate, which is fixed by pins on the tibia after a tibial cut
and serves as a reference plate.
2. A sensitive plate, which measures the moments and which lies on the
base plate.
3. A set of spacers, which allows measurements at different knee gaps.
Finally, the material used for the sensitive plate has to be:
1. Biocompatible. Biocompatibility is the quality of not having toxic or
injurious effects on biological systems. There exist different degrees of
biocompatibility, depending on the amount of time the material has to
be in contact with the human body, especially with bones and bodily fluids. Although the device operates for less than half an hour,
implantable material should be used in order to preserve the patient
safety in case of accidental release of debris.
2. Compatible with thick-film technology. Up to now, the deposition process is controlled for stainless steel based applications. The high curing
temperature during deposition limits the choice of material and prevent
the usage of metals with better properties for a force-sensing device,
such as titanium.
3. Suitable mechanical properties. The selected material must have suitable mechanical properties for a force-sensing device, i.e. a large elastic
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
26
range and a high ultimate stress. Moreover, as the device is heated
during the sensors curing, it must have these properties in annealed
conditions.
The stainless steel Bioline High-N from Sandvik, Sandviken, Sweden fulfills
the above requirements. It is certified implantable and its mechanical properties summarized in table 3.1 are perfectly suitable.
Young’s modulus
Poisson’s ratio
Yield point
Ultimate stress
200 · 103 N/mm2
0.3
430 N/mm2
740 N/mm2
Table 3.1: Mechanical properties of Sandvik Bioline High-N Annealed
The perimeter, the material and the different parts of the design having been
determined, a detailed description of the three conceived designs is now given.
3.3.1
Design I: opposed bending beams
According to the simplified biomechanical model, the knee stability can be
assessed by comparing the varus-valgus moment of the medial and lateral
condyles. Thus, the first design was inspired by a balance scale: the sensitive plate has the shape of a standard inlay into which two bending beams
reproducing the balance trays are cut (Fig.3.5). According to the flexure
formula (c.f. equation (A.22)), the varus-valgus moments created by the
contact forces are proportional to the stress and strain experienced at the
base of each bending beam, where two piezoresistive sensors are arranged in
a half Wheatstone bridge configuration.
The measurement principle was simulated using Finite Element Modelling
(FEM). 29’680 solid parabolic tetrahedrons with a length parameter of 1.5mm
compose the mesh. A 500N load is applied in the middle of the right side.
The boundary conditions are set so that the device perimeter of the bottom
face is clamped. Fig.3.6 shows the distribution of von Mises stresses (c.f.
equation B.20) in the bottom view of the device. The stresses in the sensitive area are 57N/mm2 .
Two parameters, the radius and the shift between the beginning and the
end of the beam cutout, were optimized to homogenize the stress in the
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
27
Figure 3.5: 3D model of design I
Two bending beams allow the measurement of the varus-valgus moments of the medial
and lateral femoral condyles.
sensitive areas of the device in order to minimize the stress variation along
the piezoresistive sensors (Fig.3.7):
1. A small cutout radius generates stress concentrations and a large reduces the beam width, both being able to provide stresses exceeding the
material limit. A good indicator of an homogeneous stress distribution
is the ratio between the maximal and average stresses. As this ratio
this ratio nears 1, the stress distribution becomes more homogeneous.
This ratio was therefore calculated by FEM for different cut radii and
showed that the optimal radius is 6mm.
2. As the contact point of each condyle is not expected to lie in the center
of the beam but rather in the center of the left or right part of the
device, the beam rotation axis is not perpendicular to the beam itself.
To facilitate the placement of the sensors, which should be on the beam
rotation axis where the stress is theoretically maximal, the perpendicularity has to be restored. This can be carried out by imposing a shift
between the beginning and the end of the beam cutout. To determine
the optimal shift, the stress variations along the axis perpendicular to
the beam and going by the point of maximal stress was computed by
FEM for different shift amplitudes. The variations are minimal with a
shift of 5.6mm.
At first sight, this design seems adequate. The stresses are smoothly distributed in the sensitive area and the ratio of 1.7 between the maximal and
average stresses gives a reasonably homogeneous sensitive area. Moreover,
28
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
Figure 3.6: FEM of the design I
A 500N load (F ) is applied in the middle of the right side
the sensitivity is satisfying and could be easily increased by diminishing the
beam thickness. However, an important drawback makes this design unsuitable for our application. The sensitive areas, where the sensors are supposed
to measure the varus-valgus moments, are not located at the center of the
device but at the base of the bending beam. The distance Rc (Fig.3.6) between a sensitive area and the center of the device is a source of error. When
the moments of the contact forces F1 , F2 measured by each beam are equal:
F2 (X2 − Rc ) = F1 (X1 − Rc ) ,
(3.4)
X1 , X2 being the lever arm respective to the device center, the net varusvalgus moment is:
(3.4)
Mnet = F2 X2 − F1 X1 = (F2 − F1 )Rc .
(3.5)
Rc being 10mm and supposing that the measured varus-valgus moment of
each contact force is 1440Nmm with respective forces of 80N and 120N, and
respective lever arms of 28mm and 22mm, Mnet is 400Nmm. This means a
8% error relative to the sum of the effective lateral and medial varus-valgus
moments. In practice, additional experimental errors will affect the device
accuracy, thus bringing the final measurement error surely above 10%. To
overcome this problem, the location and amplitude of the femoral contact
forces have to be measured separately.
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
29
Figure 3.7: Design optimization
The radius and the shift between the beginning and end of the cutouts were optimized to
have maximal homogeneous stress areas
3.3.2
Design II: open load cell
To measure the amplitude and location of the femoral contact forces, three
measurement points per condyle are necessary. The simplest way to realize that is to have a defined medial and lateral contact area attached to a
frame by three deformable bridges (Fig.3.8). When the device is loaded, the
sum of the stresses experienced by the three bridges is proportional to the
amplitude of the applied force whereas the ratio determines its location. To
perform correctly, however, such a device needs a large and strong frame,
rigid enough to absorb and homogeneously distribute the load. The room
being restricted in our application, this condition can not be ensured and the
measurements could depend on the location of the contact points between
the frame and the tibial base plate. For a good accuracy and reliability of the
measurements, the contact points between the plates must be mechanically
well defined. Therefore, two sensitive plates and two sets of three balls are
used to avoid statically indeterminate conditions.
The thickness of the sensitive plates is 3mm. The contact areas have an internal diameter of 19mm. The bridges are 4mm wide to leave enough space
for the electrical connections, as well as 5mm long and 1mm thick to be
sensitive enough to the deformations. The large contours at the bridge extremities avoid stress concentrations. Two piezoresistive sensors are placed at
each side of each bridge, with two working in compression and two in tension.
A full Wheatstone bridge can thereby be used, increasing the measurement
sensitivity and avoiding temperature drift. To prevent the femoral condyles
from being damaged by the cuts, a plastic hat could be placed on the top of
the sensitive plates.
30
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
Figure 3.8: 3D model of the design II
A circular contact area is attached to the frame of the device by three deformable
bridges, thus allowing the measurement of the amplitude and the location of the
compressive forces.
The measurement principle is simulated by FEM analyses for one single sensitive plate (Fig.3.9). The mesh is composed by 28’596 solid parabolic tetrahedrons with a length parameter of 1.5mm. The boundary conditions are
set so the ball seats are clamped. A 500N load is applied once at the center
and once shifted by half of the radius of the sensitive area to exemplify the
determination of the contact point.
These FEM analyses demonstrate the suitable sensitivity of the device. With
a 500N centered load, each bridge experiences stress of 120N/mm2 . When the
load is not centered, the closest bridges from the application point undergo
almost twice more stress (160N/mm2 ) than the most distant (70N/mm2 ).
With a relative difference of 8%, the sum of the stress in both situations
(360N/mm2 and 390N/mm2 ) can be considered equivalent in compliance
with the fact that the amplitude of the applied load is the same.
Despite the apparent suitability, this design has two major problems. Firstly,
the sensitive area is too limited. According to [8] the rollback of the lateral
condyle is about 10mm for a 0-90◦ flexion and 22mm for a 0-120◦ flexion. Although these movements can hold in the contact areas, there is no significant
safety margin. Moreover, the device is intended for use with pathological
knees where deviations from this standard can be expected. Secondly, the
contact with the balls can be a source of error. In practice, friction between
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
31
Figure 3.9: FEM of the design II
A 500N load applied once at the center, once shifted to the right, shows the sensitivity as
well as the functioning
the balls and the base plate generates moments in the bridges which have
not been taken into account so far. The friction force is proportional to the
reaction force (F ) which creates the moment in the bridge. Therefore, the
ratio between the moment that has to be measured and the moment due to
friction is given by:
µd1
µF d1
=
.
(3.6)
F d2
d2
The lever arm of the friction moment (d1 ) is equivalent to the device thickness, i.e. 3mm. The distance between a bridge and the closest contact point
varies from 10mm to 20mm (d2 ). A typical metal-to-metal friction coefficient
(µ) being 0.2, the friction moment in a bridge corresponds to 3% to 6% of
the effective moment. The device having six bridges, the total measurement
error due to friction is definitely not acceptable. To further optimize the design, the contact area must be increased and the disturbances due to friction
moment minimized.
3.3.3
Design III: integrated bridges
To maximize the contact area, the three bridges needed to measure the location and the amplitude of the femoral contact forces must be shifted to
32
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
the device border (Fig.3.10). The bridges are 4mm wide and 4mm long to
have enough room for the sensors and their connections and 1mm thick to
ensure a good sensitivity. The bridge cutouts have been optimized by FEM
in order to suppress stress concentrations while keeping a sufficiently large
contact area. The fillet under the bridges has a 1mm radius, which follows
the empirical rule stating that a fillet as large as the bridge thickness allows
avoiding stress concentrations. A ball is inserted in each pillar extremity to
ensure mechanically well defined contact points between the tibial base plate
and the sensitive plates. Moreover, since these balls allow rotations, torsion
is avoided and the bridges undergo pure bending.
Figure 3.10: 3D model of design III
The three bridges are placed at the device border to maximize the sensitive area and a
symmetrical bridge is used to minimize error due to friction moments. When a load F is
applied on the device, three reaction forces Ri (i = 1, 2, 3), whose amplitude depend on
the amplitude and location of the original load, are generated. The deformation of each
bridge due to a single reaction force is then measured.
The measurement principle is as follows: when a load F is applied in the
2 and R
3 are generated at the
1, R
sensitive area, three reaction forces R
bridge pillars. The amplitude of those reaction forces is directly related
to the location and amplitude of the applied load through the equilibrium
equations:
i + F = 0
R
i
i + X
∧ F = 0 ,
i ∧ R
X
(3.7)
i
i , i = 1, 2, 3 are the respective lever arms. As all the forces are
where X
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
33
perpendicular to the plate surface, the previous vectorial equations come
down to three independent scalar equations:
x1 R1 + x2 R2 + x3 R3 − xF = 0
y1 R1 + y2 R2 + y3 R3 − yF = 0
R1 + R2 + R 3 − F = 0 ,
(3.8)
which can be solved for F , x, y.
F = R 1 + R2 + R3
x1 R1 + x2 R2 + x3 R3
x =
R1 + R2 + R3
y1 R1 + y2 R2 + y3 R3
y =
R1 + R2 + R3
(3.9)
Due to the difference of rigidity between the bridges and the rest of the sensitive plates, each bridge is deformed by the reaction force experienced by
its own pillar. Everything occurs as if each bridge was laterally clamped and
a single force applied at its center. In such situation, one compression and
one tension domain appears at each side of the bridge pillar (Fig.3.11). The
amplitude of the reaction forces can be measured with four piezoresistive
sensors placed at these specific locations (c.f. appendix A) and arranged in a
full Wheatstone bridge. The location and amplitude of the applied load can
then be calculated thanks to equation (3.9).
Figure 3.11: Deformation of a single bridge
The sides of the bridge are clamped and a load is applied at the center. Two compression
and tension areas appear at each side of the pillar.
34
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
With this design, the contact area is defined by a triangle, whose edges are
located at the pillar centers. This triangle has a base of 22mm and a height
of 36mm, which is much larger than with the open load cell design. Another
advantage of such a bridge configuration is the self-compensation of error due
to friction moments. As the effect of friction has the same amplitude but an
opposite sign at each side of a single bridge, it is electronically cancelled out
by the Wheatstone bridge.
Fig.3.12 is a typical simulation by FEM of the device performance. 28’735
solid parabolic tetrahedrons with a length parameter of 1mm compose the
mesh. The boundary conditions are set so the pillar extremities allow rotations but not translations. A 500N load is applied once centered and once
posteriorly shifted to illustrate the measurement principle. The maximal
compressive von Mises stress is 150N/mm2 and the maximal tensile stress
is 210N/mm2 when the load is centered. This asymmetry comes from the
overall bending of the sensitive plate, which is added on the bridges, thus
decreasing the compression and increasing the tension stresses. However, this
asymmetry is not a problem in practice since contributions equal in amplitude
and sign cancel each other due to the full Wheatstone bridge configuration.
Figure 3.12: FEM of the design III
A 500N load applied once at the center, once posteriorly shifted, shows the sensitivity as
well as the working principle
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
35
Finally particular attention must be paid to the balls: a very small ball
diameter creates huge contact pressure which can tear the tibial base plate.
The hertzian theory is therefore used to verify that the selected material and
geometry support the loads involved in this application. From appendix B,
it is known that the maximal pressure of a sphere in a spherical seat is given
by
F
(R1 − R2 )2
1 3 6
,
(3.10)
Pmax =
π π 2 (K1 + K2 )2 R12 R22
Ki =
1 − νi2
πEi
i = 1, 2 .
E is the Young’s modulus, ν the Poisson’s ratio, i indexes the two bodies, F
the load, R1 and R2 the radius of the ball and its seat. From this maximal
contact pressure, the corresponding effective stress or von Mises stress, which
can be compared to the material specifications given by the manufacturer,
can be calculated using the relationship (c.f. appendix B):
max
σef
f = 0.6Pmax .
(3.11)
Since the Sandvik High-N stainless steel would not support the contact pressure, titanium has been chosen for its biocompatibility and its relatively low
Young’s modulus (c.f. Table 3.2), which decreases the maximal pressure according to equation (3.10).
Young’s modulus
Poisson’s ratio
Yield point
Ultimate stress
114 · 103 N/mm2
0.34
870 N/mm2
950 N/mm2
Table 3.2: Mechanical properties of Titanium Grade 5 ELI
The diameter of the balls is 3mm and corresponds to the largest diameter
allowing press-fit in the pillars. The seat in the base plate is 3.5mm and
follows from a trade off between the pressure amplitude and the manufacturing precision. On one hand, the seat diameter should be as close to the ball
diameter as possible to maximize the contact area and therefore minimize
the contact pressure. On the other hand, it should be large to minimize
the errors induced by the manufacturing accuracy: a shift between the balls
and the seat location would lead to reaction forces not parallel to the pillars,
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
36
thus inducing measurement errors. As the selected steel balls are normally
used in ball bearings and can support a pressure as large as 4’200N/mm2 before reaching their yield point, only the titanium plate has to be inspected.
With the numerical values presented above, the 870N/mm2 yield point of
titanium is reached with a load of 270N: more than half of the maximal load
can be supported by a single pillar without yielding, which is sufficiently safe.
In conclusion, this design fulfills the requirements and shows important decisive advantages:
• Accurate measurement of force amplitude and location
• Mechanical decoupling between the medial and lateral sides
• Maximal contact area
• Minimal parasite effects (temperature drift, friction moments)
• Small size and thickness
• Possibility to keep the patella at its anatomical place during the measurement
• Sterilizable
This last design has therefore been considered as optimal and a series of
prototypes were built.
Extension of the sensitive area
Although the sensitive area has been maximized, the contact points of the
femoral condyles can be located close to the lateral device borders due to deformities or unusual anatomy. Such cases would be out of the sensitive area
and therefore not measurable. In addition to this, the sensitive plate should
be fastened to the base plate in order to avoid lift-off during manipulations
or in absence of compressive forces.
To address these two issues, a fixation mechanism was developed (Fig.3.13).
It has a T-shape whose pillar is screwed to the base plate and whose arms
cover the posterior medial bridge of each sensitive plate. A screw with a
spherical head placed at each arm’s extremity allows the bridges to be fixed.
The spherical screw head enables rotations, thus avoiding torsion in the
bridge. With this system, the posterior medial bridge can measure vertical
reaction forces in both directions, which allows the measurement of contact
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
37
Figure 3.13: Fixation mechanism
A T-shape mechanical part allows the posterior medial bridge of each sensitive plate to
be fastened to the tibial base plate.
forces located close to the lateral edge of the device. The same calibration
model can be used since the only change is the sign of the output voltage
reflecting the direction of the reaction force. In addition to extending the sensitive area, this fixation mechanism enables the sensitive plates to be rigidly
fastened to the tibial base plate. Thus, the different parts constituting the
device can be introduced as one piece into the knee, which improves the
ergonomics of the device.
Spacers
As previously mentioned, a set of medial and lateral spacers are needed to
adapt the device thickness to the patient-specific tibiofemoral gaps. From
the engineer’s point of view, the best solution would be to intercalate spacers between the tibial base plate and the sensitive plates. By doing so, the
femoral condyles are directly in contact with the sensitive plates, thus ensuring an optimal output signal. However, this solution would significantly
diminish the device ergonomics since the fixation mechanism would need to
be replaced each time a thicker spacer is used. To overcome this disadvantage, spacers should be placed on the top of the sensitive plates. Particular
attention must therefore be paid to the shape of the spacers and the material
used to keep accurate measurements.
Thin adaptor spacers (2mm) are placed directly on the top of the sensitive
plates to ensure a correct transmission of applied loads to the sensitive area
(Fig.3.14). Medial, lateral and posterior cutouts allow accommodating the
wires and the fixation mechanism. The bottom surface follows the contour of
the sensitive area to enable the deformation of the sensitive plates. If these
38
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
adaptor spacers would lie on the bridges, applied loads would be withstood
by the reaction forces in the bridge pillars without producing any beam deformation. Two rectangular extrusions designed to fit in the sensitive plate
cutouts avoid rotations and translations of the spacer. Finally, the top surface has an anterior elliptical extrusion which serves as an attachment point
for the additional block spacers (Fig.3.14). These latter have thicknesses
ranging from 1mm to 10mm. A posterior cutout allows accommodating the
fixation mechanism and a bottom anterior conical hole enables the block
spacers to be plugged into the adaptor spacers.
(a) Top view
(b) Bottom view
Figure 3.14: Spacers
Thin adaptor spacers, onto which block spacers of different thicknesses can then be
plugged, are used to ensure a correct transmission of applied loads to the sensitive area.
The reliability of the load transmission through the spacers depend not only
on the geometry but also on the material used. To ensure an optimal selection, the contact pressure distribution at the bottom surface of a spacer
was analyzed by FEM for different materials. The model consisted of a 5mm
thick spacer placed on a single sensitive plate. The contact condition was
carried out by a penalty method. The meshes of the spacer and the sensitive
plate were composed by 5931 and 4927 tetrahedron elements respectively,
with a length parameter of 1mm. A 100N vertical force was applied to the
top of the spacer, at the center of the sensitive area. The contact pressure
distribution was then calculated for four different materials: stainless steel,
aluminium, and polyethylene with a 10GPa or 1GPa Young modulus.
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
(a) Stainless steel
(b) Aluminium
(c) PE 10GPa
(d) PE 1GPa
39
Figure 3.15: Spacers made of different materials
Pressure distribution at the bottom surface of spacers made of stainless steel, aluminium,
or polyethylene with a Young modulus of 10GPa and 1GPa.
40
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
The results are that hard materials, such as stainless steel or aluminium,
hardly deform and the main contact points are located at the border of the
contact area (Fig.3.15). This situation should be avoided since high stress
concentrations would be generated close to the measurement bridges. With
softer material, such as polyethylene, the spacer deformation is much larger.
Thus, a circular contact area, whose center corresponds to the point of application of the load, can be observed and the pressure concentrations close to
the bridges disappear. Spacers must consequently be made of polyethylene
or other biocompatible materials with similar mechanical properties.
Figure 3.16: Variation of stress distribution
Comparison between the top and bottom surface stress distribution when the applied
load is being laterally shifted.
Finally the issue of accuracy loss due to spacers must be addressed. The
precision of the force amplitude measurement should not be affected since
the device provides an integral measurement, which is by definition independent on the force distribution. However, one may imagine that intercalating
spacers between the femoral condyles and the sensitive plates can reduce
the accuracy of the force location measurement. As the force-sensing device
measures the location of the gravity center of applied loads, accuracy loss
for the position measurement should not happen as long as the gravity centers of the stress distributions on the top and bottom surfaces of the spacers
are the same. To verify that, the stress distributions were compared for a
3.3. DEFINITION, EVALUATION OF POSSIBLE DESIGNS
41
100N load being shifted from the center to the border of the sensitive area
by steps of 5mm. For each step, the gravity center calculated by the FEM
software was identical for the top and bottom stress distributions. Fig.3.16
also demonstrates this equivalence in a graphical way: the symmetry center
of the stress variation along a horizontal axis is the same for both distributions. Therefore, no accuracy loss due to the intercalation of spacers should
be expected.
To conclude this chapter, the design of the complete device is shown in an
exploded three-dimensional view (Fig.3.17).
Figure 3.17: Complete device
Exploded three-dimensional view of the complete device
42
CHAPTER 3. FORCE-SENSING DEVICE DESIGN
Chapter 4
Thick-film piezoresistive sensors
4.1
Piezoresistive effect
By definition, piezoresistive sensors are elements whose resistance varies in
response to a mechanical stimulation. They can therefore be considered as
strain gauges, akin to metallic gauges, whose principle has been shortly explained in section 3.2.3. A more elaborate technique is nevertheless used in
order to obtain a higher strain sensitivity as well as a good quality of the
gauge bond to the substrate, usually a source of difficulties and errors with
foil gauges. A thick-film piezoresistive bridge, directly screen-printed and
fired onto the steel substrate, was used. The sensing thick-film resistors are
typically composed of 85% of glass (P bO − SiO2 − B2 O3 − Al2 O3 ) and 15%
of conductive oxide particles (RuO2 and P b2 Ru2 O6 ). After sintering, the resistor material consists of an insulating glass matrix, in which the conductive
particles form a percolating network. Charge transport between adjacent
particles is governed by tunnelling through a very thin (ca. 1nm) insulating
layer. The interparticle resistance depends directly on the average distance
d separating two charged particles. Therefore, when the sensor is strained,
the average distance d is modified and the resistance varies accordingly. The
tunnelling effect and the local strain inhomogeneity [48, 49] account for the
relatively high sensitivity ("gauge factor") of thick-film resistors, ca. 12 vs.
ca. 2 for metal gauges.
A thick-film sensing bridge on steel requires at least three different materials:
the insulating dielectric, the conductor and the piezoresistor. Usually, a
fourth protective glassy layer is applied over the circuit to improve chemical
and electrical stability.
43
44
4.2
CHAPTER 4. THICK-FILM PIEZORESISTIVE SENSORS
Thick-film technology
To produce thick-film sensors, the screen printing technique is used, whereby
the thick-film materials, formulated in paste form (active material, binder,
solvent and additives), are printed onto the substrate through a screen which
defines the pattern. A typical thick-film screen is a fine metallic mesh
mounted on a frame and coated by a photosensitive emulsion. The electronic
pattern is printed on a transparent page and transferred to the thick-film
screen by an ultraviolet light exposition. The screen, which has now open
and closed areas defining the desired pattern (Fig.4.1(a)), is mounted on a
screen-printing machine at a distance of about 0.5mm from the substrate. A
squeegee pushes the thick-film paste over the screen, and thereby dispenses
a well-defined amount of paste onto the areas of the substrate defined by
the screen (Fig.4.1(b)). The paste is then dried at 150◦ C to eliminate the
solvents, allowing further printing operations. After printing and drying one
or several layers, the thick-film materials are fired in an oven, using a temperature profile having typically a ten-minute plateau at 850◦ C (Fig.4.1(c),
4.1(d)). Note that the thick-film process is not only used with piezoresistive
elements but also in a wide range of applications involving piezoelectric, capacitive, photovoltaic, thermal, magnetic or chemical sensors [50, 51].
Thick-film piezoresistive sensors are usually printed on ceramic substrates
such as alumina, due to their thermal stability and chemical inertness [52].
However, the use of ceramic substrate has several limitations such as a poor
machinability, the incapacity of withstanding high strain or the brittle nature
of ceramic. In the nineties, stainless steel was successfully used as a substrate
[53, 54, 55], thus opening the way to more robust and precise metal-based
applications. Current developments are focused on reducing the firing temperature of thick-film pastes to allow employing substrates with excellent
mechanical properties, such as titanium [56], while examining the effect of
the substrate (thermal and chemical properties) on the resistive and piezoresistive behavior [57, 58, 59].
4.3
Mechanical properties
A current drawback of thick-film technology on steel is the high required firing
temperature (850◦ C), which is not compatible with most steel strengthening
mechanisms such as cold work, martensitic transformation or precipitation
hardening. Therefore, a nitrogen-containing biocompatible austenitic stainless steel was used: Sandvik Hi-N, where the nitrogen content imparts a
4.3. MECHANICAL PROPERTIES
45
(a) Thick-film screen
(b) Paste deposition
(c) Oven
(d) Sensor firing
Figure 4.1: Screen printing process
considerable solution strengthening effect, which is not affected by the thickfilm firing process. To test the compatibility between the selected steel and
the thick-film piezoresistive sensors, deformable membranes have been manufactured (Fig.4.2(a)). Such pressure sensor is a reference device for material
characterization of the Laboratoire de Production Microtechnique, EPF Lausanne, Switzerland, the collaborative institute in charge of the production of
the sensors.
Different pressure magnitudes were applied stepwise on the membrane generating radial stresses (σr ) up to 600MPa. The relative signal drift reported in
figure 4.2(b) is lower than 0.1% for all the applied stresses. The softer stainless steel DIN 1.4435, from which is branched off the biocompatible steel DIN
1.4441 used for numerous surgical tools such as scalpels, pliers or chisels, has
standard mechanical properties and is presented in the diagram for comparison. The obtained result demonstrates the proper functioning of the device
and therefore the compatibility of the technique with the selected stainless
steel.
46
CHAPTER 4. THICK-FILM PIEZORESISTIVE SENSORS
(a) Deformable membrane
(b) Signal drift
Figure 4.2: Deformable membranes
4.4
Custom low-temperature dielectric
Due to the high coefficient of thermal expansion (CTE) of the austenitic
Sandvik Hi-N steel (16.5 10−6 /◦ C), delamination due to thermal mismatch
with the thick-film layers may occur during the cooling phase following firing.
Extensive problems were not observed on the simple membranes described in
the previous section, which only comprise a dielectric - conductor - piezoresistor sequence, although local chipping at the edges of the printed dielectric
layer indicated extensive compressive stresses. Our force-sensing device, however, is more complex than the membranes and requires additional dielectric
and conductor layers to allow electric cross-overs. The resulting stress buildup proved fatal to the devices: extensive spallation in the thick-film circuits
occurred in these cross-over zones.
Therefore, cross-overs were made with different materials: a commercial lowfiring fritted silver conductor, together with a special low-stress dielectric
developed at EPFL. This low-firing dielectric consists of a dispersion of alumina powder in a low-melting lead borosilicate glass having a high CTE.
The high CTE, together with the low softening temperature, results in very
little additional stresses being developed in the cross-overs: no spallation was
observed with the new materials. One must note that the present state of
thick-film technology does not allow the use of these materials for the main
insulating dielectric layer between the steel and the sensor circuit.
Chapter 5
Calibration and intrinsic accuracy
5.1
Calibration method
The calibration of a sensitive plate consists in establishing the numerical
relationship which converts the three measured voltages (M1 , M2 , M3 ) into
the corresponding location (x, y) and amplitude (F ) of the applied force.
The calibration model results directly from equation (3.9), which describes
the measurement principle of the device, and is expressed by:
F = C11 M1 + C12 M2 + C13 M3
x =
C21 x1 C11 M1 + C22 x2 C12 M2 + C23 x3 C13 M3
C11 M1 + C12 M2 + C13 M3
y =
C31 y1 C11 M1 + C32 y2 C12 M2 + C33 y3 C13 M3
.
C11 M1 + C12 M2 + C13 M3
(5.1)
The three first calibration coefficients (C11 , C12 , C13 ) correspond to the proportionality factor existing between the output voltage and the reaction force
amplitude of each bridge. The six last coefficients quantify the deviation of
the experimental reality from the theoretical model in the x (C21 , C22 , C23 )
and y (C31 , C32 , C33 ) directions. In an ideal case, they should be 1.
To determine these nine coefficients, 16 points of measurements are used:
four loads evenly distributed in the range 0-500N and four locations evenly
distributed on the sensitive area. As the determination of the six last calibration coefficients depends on the three first, the computation based on a
least square method is performed in two steps. Table 5.1 shows an example
of a typical calibration matrix. As the most important deviation of the six
last coefficients from the ideal value of 1 is 5% only, the calibration model is
47
48
CHAPTER 5. CALIBRATION AND INTRINSIC ACCURACY
considered correct and appropriate.
4.757
1.009
1.048
4.508
1.007
0.998
4.580
1.006
1.000
Table 5.1: Example of a calibration matrix
5.2
Intrinsic accuracy
The intrinsic accuracy of the device was evaluated by loading the sensitive
area with 18 weights ranging from 0N to 500N, applied at 20 different locations evenly distributed (Fig.5.1). The positioning of the tip of the mechanism supporting the weights was controlled by a micrometer table (Fig.5.2).
For each location, the different weights were applied incrementally.
Figure 5.1: Measurement points for the accuracy study
Figure 5.3 compares the measured force amplitudes and applied weights. The
close-to-one slope (1.0009) and confidence parameter (1) of the linear regression validates the measurement principle and demonstrates the absence of
systematic errors. The absolute difference between the measured and applied loads and locations are shown in the figures 5.4(a), 5.4(b) and 5.4(c).
The maximum force amplitude and location error among the 360 measurements were 2.6N and 0.8mm, whereas the mean absolute errors were 0.7N
5.2. INTRINSIC ACCURACY
49
Figure 5.2: Set-up used for the accuracy study
and 0.3mm respectively. Note that the location measurement error decreases
with increasing load. Since the location computation is based on a ratio between the bridge voltages, the larger each voltage is, the better defined is the
ratio. The error of the applied weights (0.01N) and locations (0.001m) being
Figure 5.3: Force amplitude vs applied weight
50
CHAPTER 5. CALIBRATION AND INTRINSIC ACCURACY
negligible, the measured deviations characterize the intrinsic accuracy. The
device thus offers an 0.5% full scale accuracy for the force amplitude measurement and a submillimeter accuracy for the force location. Such accuracy
is comparable to that of various commercial force-sensing devices based on
strain gauge technology and can be considered as excellent.
Since the passive compression forces of a human knee joint are expected to
be below 100N, a specific calibration can be performed to decrease the force
amplitude measurement error in this range. The coefficients obtained from
the calibration of the same prototype with four loads ranging from 0N to
100N instead of 0N to 500N are summarized in table 5.2 and are consistent
with their equivalent in table 5.1. Furthermore, the coefficients characterizing the deviation from the calibration model are again very close to the ideal
value of 1, thus confirming the soundness of the calibration procedure.
4.796
1.024
1.037
4.568
1.008
1.001
4.465
1.004
1.000
Table 5.2: Calibration matrix for the range 0-100N
Figures 5.5(a), 5.5(b), 5.5(c) show the absolute difference between the measured and applied loads and locations with the new calibration. This time,
the maximum force amplitude and location error were 5.6N and 0.8mm,
whereas the mean absolute errors were 1.0N and 0.3mm respectively. As
expected, the location measurement errors were not affected by the new
calibration while the force amplitude error decreased in the range 0-100N
and increased in the range 100-500N. However, the mean force amplitude
error remains comparable to that previously computed, thus demonstrating
that changing the calibration range amounts to redistributing the total error. With a maximal measurement error of 1.5N in the range 0-100N, the
measurement accuracy of the force amplitude is below 2%, which is suitable
for the intended application.
5.2. INTRINSIC ACCURACY
(a) Absolute force error
(b) Absolute x location error
(c) Absolute y location error
Figure 5.4: Measurement errors with a calibration in the range 0-500N
51
52
CHAPTER 5. CALIBRATION AND INTRINSIC ACCURACY
(a) Absolute force error
(b) Absolute x location error
(c) Absolute y location error
Figure 5.5: Measurement errors with a calibration in the range 0-100N
5.3. ACCURACY IN THE EXTENDED SENSITIVE AREA
5.3
53
Accuracy in the extended sensitive area
To verify the proper device functioning in the extended sensitive area created
by the fixation mechanism (c.f. section 3.3.3), the intrinsic accuracy was also
evaluated close to the lateral edge. The same experimental set-up as in the
previous section was used. The device was loaded with 9 weights ranging
from 0N to 100N applied at 15 different locations evenly distributed in the
extended sensitive area. Figures 5.6(a), 5.6(b), 5.6(c) show the absolute
difference between measured and applied loads and locations. The maximal
force amplitude and location errors were 1.8N and 1.2mm, whereas the mean
absolute errors were 0.5N and 0.3mm respectively. With three values greater
than or equal to 1mm, the accuracy of the location measurement is slightly
diminished. However, these errors were observed only with small weights,
i.e. at low output voltage, and did not affect the average measurement error.
It can thus be concluded that the accuracy close to the edge of the device is
equivalent to that in the center.
5.4
Accuracy with spacers
In section 3.3.3, where the design of the spacers is presented, it has been
concluded that the measurement accuracy is theoretically not affected by
the use of spacers placed on the top of the device. To verify that conclusion in practise, the device was loaded with four weights ranging from 0N
to 100N, applied at five different locations, without spacer and with spacers
of 5mm and 10mm thickness. The maximal error, i.e. the maximal absolute difference between the measured and applied loads, was determined for
each measurement condition. Fig.5.7 shows that the use of spacers slightly
increased the measurement error, which can be due to imperfect manufacturing or border effects creating an asymmetric load distribution around the
point of application. However, with maximal errors of 1.4N and 1.1mm, the
accuracy is still very satisfying and the ergonomic benefit of these top spacers
are more important than the measured loss of accuracy.
5.5
Calibration and autoclave sterilization
Finally, the influence of sterilization on the calibration had to be evaluated.
The device was loaded again with four weights ranging from 0N to 100N
applied at five different locations before and after steam sterilization (121◦ ,
100% humidity, 20min.). No difference in measurement errors was found
(Fig.5.8), thus demonstrating the autoclavability of the device.
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CHAPTER 5. CALIBRATION AND INTRINSIC ACCURACY
(a) Absolute force error
(b) Absolute x location error
(c) Absolute y location error
Figure 5.6: Measurement errors in the extended sensitive area
5.5. CALIBRATION AND AUTOCLAVE STERILIZATION
Figure 5.7: Accuracy loss due to spacers
Figure 5.8: Influence of sterilization on the calibration
55
56
5.6
CHAPTER 5. CALIBRATION AND INTRINSIC ACCURACY
Plastic deformation
For safety purposes, the largest load the device can bear without being irreversibly damaged — that means the load causing a plastic deformation, a
calibration loss and therefore a wrong diagnosis — had to be experimentally
determined. To evaluate this effective elasticity limit, the force-sensing device was loaded with a series of forces ranging from 500N to 2000N by steps
of 250N. These forces were applied at the gravity center of a sensitive plate
by a 12cm diameter tip driven by a hydraulic testing machine, a 858 Bionix
from MTS Systems Corporation, Eden Prairie, USA (Fig.5.9). For each step,
the nominal force was reached with an average loading speed of 15N/s and
was then sustained for 5s before releasing.
Figure 5.9: Set-up used for the plastic deformation test
Fig.5.10 compares the force amplitude measured by the load cell of the testing machine and by the device, while Fig.5.11 shows the signal drift, which
corresponds to the difference between both. The device signal significantly
deviated from the ideal elastic behavior with forces over 1500N. Considering
the measurement range of the device (0-500N), the safety factor is 3, which
is sufficient according to empirical designing rules.
5.6. PLASTIC DEFORMATION
Figure 5.10: Comparison of MTS forces and device measurements
Figure 5.11: Signal drift during plastic deformation
57
58
CHAPTER 5. CALIBRATION AND INTRINSIC ACCURACY
In summary, the theoretical measurement principle was validated by the calibration procedure and the obtained coefficients. Furthermore, the 0.5% full
scale accuracy and the safety factor of 3 meet the current industrial standards and makes the device reliable. The accuracy in the extended sensitive
area and with the use of spacers is slightly reduced in practise, but still very
satisfying for the application. Finally, autoclave sterilization does not influence the calibration. The device design has therefore been validated and
the evaluation of its ability to help the surgeon in ligament balancing is now
assessed with in-vitro studies.
Chapter 6
In-vitro study
Three different types of experiments were performed in order to validate
the device design and to evaluate the biomechanical influence of different
surgical actions, such as a patellar eversion or a ligament release, on the
ligament balance.
6.1
Control experiment with a plastic model
To assess the suitability of the device for the purpose of ligament balancing,
the prototype was introduced in a plastic knee joint equipped with adjustable
springs. These latter simulated the collateral ligaments and the adjustingscrews of the side mechanisms allowed varying the spring tension (Fig.6.1).
To validate that the varus-valgus moment measurements provided by our
device agree with defined imbalances, different spring tensions representing
ten levels of medial and lateral imbalance were applied. According to laws
of mechanics, it exists a linear relationship between these spring tensions
and the net varus-valgus moments of the tibiofemoral contact forces and the
corresponding proportionality factor is the lever arm of the spring forces.
The expected linear relationship between the measured net varus-valgus moment of the contact forces and the spring tensions was experimentally verified
(Fig.6.2). Furthermore, the measured proportionality factor (46mm) corresponded to the real lever arm (52mm) with a relative error of 13%. This
deviation is due to the cumulative effect of the intrinsic accuracy of the device, the adjustment uncertainty of the spring tension and the play in the
mechanical fixation of the springs. The agreement between the theoretical
expectations and the effective measurements demonstrates the device suitability for imbalance characterization in a well-controllable environment.
59
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CHAPTER 6. IN-VITRO STUDY
Figure 6.1: Plastic knee joint model
Adjustable springs simulated the collateral ligaments and the adjusting-screws of the side
mechanisms allowed varying the spring tension
Figure 6.2: Imposed imbalances and measured varus-valgus moments
The expected linear relationship between the measured net varus-valgus moment of the
contact forces and the spring tensions was experimentally verified
6.2. IN-VITRO TRIALS
6.2
61
In-vitro trials
In order to verify the suitability of the range of measurement of the device
and the consistency between the measurements and the surgeon’s perception,
the prototype was tested in two cadaver specimens.
In the first experiment, the device was installed in the knee gap after a tibial cut of about 6mm. The medial and lateral femoral contact forces and
the net varus-valgus moment were measured during a ligament release procedure. When no external forces were applied, the measured contact forces
ranged from 40N to 70N. When the surgeon manually applied varus-valgus
loads comparable to those that would be applied during a standard TKA, the
maximal contact force reached 350-400N. Thus, the measurement range of
the device (0-500N) is appropriate. The surgeon then performed a medial ligament release guided by the device measurements until the net varus-valgus
moment was reduced from an initial imbalance of 1.25Nm to 0.15Nm. The
obtained ligament balance was qualitatively consistent with the surgeon’s
perception of a “balanced knee”.
In the second in-vitro trial, the tibiofemoral forces and moments were measured in a balanced and imbalanced condition. Furthermore, five 90◦ knee
flexions were performed with two different degrees of ligament balance, which
were realized using a) a 3mm lateral and medial spacers and b) a 6mm lateral
spacer and a 3mm medial spacer. According to the surgeon’s judgment the
second condition was better balanced than the first. In the balanced knee
condition, a lateral and a medial force amplitude of 24N and 22N were measured. The relative difference of the respective varus-valgus moments was
6%. In the imbalanced condition, the lateral and medial force amplitudes
were 36N and 9N, and the relative difference of the respective varus-valgus
moments was 60%. These results indicate that device measurements reflect
the surgeon’s perception. The averaged forces and moments measured during
the flexion experiments are shown in Fig.6.3. In agreement to the surgeon’s
opinion, the second condition exhibits a relative varus-valgus moment significantly closer to 0.
In conclusion, the range of measurement of the device is suitable and the
measurements provided are in agreement with the surgeon’s perception.
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CHAPTER 6. IN-VITRO STUDY
(a) Imbalanced
(b) Better balanced
Figure 6.3: Contact forces and moments during knee flexion
Tibiofemoral contact forces and varus-valgus moment during 90◦ knee flexions with two
different degrees of ligament balance
6.3. IN-SITU EVALUATION
6.3
63
In-situ evaluation
Following these promising preliminary experiments, a complete in-vitro study
was carried out. The three primary goals were:
1. To evaluate the in-situ functioning and potential clinical advantages of
the novel force-sensing device.
2. To identify the biomechanical parameter that the surgeon intraoperatively assesses during ligament balancing. Each measurement system
described in section 2.4 and aimed at providing a quantitative measurement of the ligament imbalance measures a different biomechanical parameter: Winemaker [44] measures extension gaps, Morris et al.
[41] compressive forces, Takahashi et al. [39] and Wallace et al. [36]
pressure and finally Attfield et al. [35] angular deviations of a scalelike device. This indicates that there is no standard interpretation of
what the surgeon intuitively calls ligament balancing in biomechanical
terms.
3. To quantify the effect of collateral ligament release in terms of forces.
Even though ligament release is a commonly used surgical action to
correct imbalance, its biomechanical effect in terms of knee joint forces
is poorly documented.
6.3.1
Method
The force-sensing device was tested in six human cadaver knees from donors
with an average age of 82 years (63 to 90). The surgical preparation of
each specimen consisted of the two first steps of TKA, i.e. accessing the
joint with a medial parapatellar approach followed by the resection of the
tibial plateau. The force-sensing device was then introduced (Fig.6.4) and
the specimen mounted on a knee joint loading apparatus (Fig.6.5) previously
described by Dürselen at al. [60]. This machine provides all the degrees of
freedom needed for unconstrained knee motion and allows the monitoring
of the relative angular position between the femur and tibia. Compression
loads and varus-valgus moments can be applied by using a system of weights
and pulleys. Additionally, quadriceps forces can be simulated by loading the
patellar tendon with weights.
To validate the in-situ measurement of forces, the knee joint was first loaded
in full extension with axial compressive weights ranging from 1kg to 15kg.
The sum of the medial and lateral contact forces measured by the device,
CHAPTER 6. IN-VITRO STUDY
64
(a) Before insertion
(b) Insertion
(c) After insertion
Figure 6.4: Device insertion
The insertion of the device into a knee joint is fast and easy. The elapsed between the
first and last picture was 1min.28s.
i.e. the total force transmitted through the tibiofemoral joint, was then compared to the applied loads.
Since the possibility of having the patella in its anatomical place during the
measurement is claimed to be a major advantage, the effect of a patellar
eversion on the mediolateral distribution of the contact forces was evaluated.
The patellar tendon was loaded with weights ranging from 1kg to 5kg at 0◦ ,
30◦ , 60◦ and 90◦ flexion with and without a patellar eversion. The relative
amounts of the applied load going through the medial and lateral compartments of the knee joint were measured and compared for each position and
each condition (patella everted or not). As part of the load applied on the
patella tendon was transmitted parallelly to the tibial plateau, the measurements were normalized by the perpendicular component to ensure comparable data. The sum of the relative medially and laterally transferred loads
6.3. IN-SITU EVALUATION
65
Figure 6.5: Knee joint loading apparatus
The arrows indicate the degrees of freedom of the machine, which allows unconstrained
knee motion. Compression loading (A), quadriceps force simulation (B) or varus-valgus
loading (C) can be carried out with a system of weights and pulleys.
then corresponds to 100%. The statistical significance was determined with a
sign test for paired samples (Matlab, MathWorks Inc, Natick, United States).
The second part of the study aimed at identifying the biomechanical parameter that the surgeon assesses during ligament balancing. Intraoperatively,
the surgeon manually compares the varus and valgus forces that must be
applied at the ankle to create a lateral or medial condyle lift-off. With a simplified two-dimensional model (Fig.6.6), it can be theoretically demonstrated
that this corresponds to a balancing of the medial and lateral condyle contact
forces. The model considers the five major forces involved in the varus-valgus
stability: the medial and lateral collateral ligament forces (FM L , FLL ), the
medial and lateral contact forces (FM C , FLC ) and an external varus force
(FEX ). The center of rotation, which in Fig.6.6 corresponds to the contact
point of the medial condyle, is taken as the reference for the computation of
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CHAPTER 6. IN-VITRO STUDY
moments. In this model, bones are considered as rigid bodies and ligaments
as springs, thus implying that ligament forces can be assumed constant at
a given flexion angle as long as both condyles are in contact with the tibia.
The tension in a spring-ligament would vary only when the joint starts to
open, i.e. when one condyle lifts off.
Figure 6.6: Varus-valgus loading model
A simplified two-dimensional biomechanical model of a knee joint experiencing varus or
valgus load to create a lateral or medial condyle lift-off. The five major forces involved in
the varus-valgus stability, which are the collateral ligament forces (FM L , FLL ), the
contact forces (FM C , FLC ) and the external force (FEX ), are taken into account.
The equilibrium condition for the moments yields:
XM L · FM L − XLL · FLL + XC · FLC + Y · FEX = 0
(6.1)
The resultant ligament moment MLIG is:
MLIG = XM L · FM L − XLL · FLL
(6.2)
The contact force FLC depends on the applied force FEX :
FLC = FLC (FEX )
(6.3)
6.3. IN-SITU EVALUATION
67
The combination of equations (6.1), (6.2), and (6.3) can then be written as:
MLIG + XC · FLC (FEX + Y · FEX = 0)
(6.4)
When there is no external force applied (FEX = 0), equation (6.4) gives:
MLIG = −XC · FLC (0)
(6.5)
When there is a varus load (FEX = Fvarus ) that generates a lateral condyle
lift-off (FLC = 0), equation (6.4) gives:
MLIG = −Y · Fvarus
(6.6)
The relationship between the varus load required for a condyle lift-off and
the initial lateral contact force can be deducted from equations (6.5) and
(6.6):
XC
FLC (0)
(6.7)
Fvarus =
Y
The same approach can be adopted for the case of a valgus load and a medial
condyle lift-off:
XC
(6.8)
FM C (0)
Fvalgus =
Y
With equation (6.7) and (6.8) it can finally be concluded that the relative
difference of the forces required for a condyle lift-off is equal to the difference
of the contact forces:
Relative Imbalance =
FLC (0) − FM C (0)
Fvarus − Fvalgus
=
Fvarus + Fvalgus
FLC (0) + FM C (0)
(6.9)
In order to experimentally validate this equivalence as well as to compare
this approach to the device measurements, the relative imbalance was assessed on the basis of three different parameters: 1) the weights required for
a condyle lift-off, 2) the contact forces and 3) the varus-valgus moments. The
knee joint was therefore loaded with varus and valgus forces with weights increasing from 0kg to 1kg. If the condyle lift-off was not achieved before 1kg,
larger weights were used. Since during the surgery the ligament imbalance is
assessed in full extension and in 90◦ flexion, the experiment was performed
in both positions.
In the third step, the biomechanical effect of medial collateral ligament releases was quantitatively evaluated. With interarticular spacers applying
stress to the ligaments, a minor followed by a major medial collateral ligament release was performed with the knee in full extension. The medial and
CHAPTER 6. IN-VITRO STUDY
68
lateral contact forces were recorded after each surgical action and compared
to the initial value. In order to quantify the effect of the ligament release on
the tibiofemoral alignment, the variation of the varus-valgus angle resulting
from the releases was measured as well. Finally, the initial and ultimate
contact forces were measured at 0◦ , 30◦ , 60◦ and 90◦ flexion to evaluate the
effect of ligament releases throughout the knee flexion.
6.3.2
Results
All the curves obtained during the compression loading experiment were
highly linear (r2 = 1.00) and the measured slopes ranged between 0.96 and
1.03, thus being very close to the ideal value of 1 (Fig.6.7). The average
difference between the applied and measured compressive force was 1.8N.
Thus, the in-situ force measurements are accurate and repeatable.
(a) Example of compression loading
slope
y-intercept
knee 1
1.03
-1.2
knee 2
0.98
-1
knee 3
1.03
-0.2
knee 4
0.96
-1
knee 5
1.00
0.3
knee 6
0.98
-0.5
(b) Linear regression parameters
Figure 6.7: Compression loading experiment
a) Comparison between the measured and applied forces during the compression loading
experiment for one specimen. b) Parameters obtained from the linear regressions, which
demonstrate the accuracy and reliability of the in-situ force measurement.
6.3. IN-SITU EVALUATION
69
In the patellar load distribution experiment, the relative amounts of the applied load going through the medial and lateral compartment of the knee joint
were measured. The mediolateral load distribution did not vary considerably
with knee flexion (standard deviations ranged from 3% to 8%), therefore the
laterally transferred loads were averaged over the different knee positions.
The mediolateral distribution of the patellar load was significantly different
(p=0.03) when the patella was in its anatomical place or not: one fourth
of the patellar load was shifted from the medial to the lateral side with a
patellar eversion (Fig.6.8). Additionally, it can be noted that the patella in
its anatomical place already influenced the mediolateral distribution of the
contact forces since the average laterally transferred load was 62% without
a patellar eversion.
Figure 6.8: Effect of patellar eversion
Relative laterally transferred loads during the patellar load distribution experiment,
showing that the patellar eversion significantly affected the mediolateral distribution of
the contact forces. The grey and black horizontal lines correspond to the average loads
with the patella respectively in place or everted.
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CHAPTER 6. IN-VITRO STUDY
A typical curve obtained during a varus-valgus loading (Fig.6.9) presents
three distinct areas: 1) the lateral condyle is in contact; 2) both condyles
are in contact; 3) the medial condyle is in contact. In each area, a linear
relationship between the applied and measured varus-valgus moments was
found. The slope was lower in the situation where only one condyle was in
contact than where both were.
Figure 6.9: Varus-valgus loading experiment
Comparison between the applied and measured moments during varus-valgus loading,
where three different situations can be distinguished: 1. the lateral condyle is in contact;
2. both condyles are in contact; 3. the medial condyle is in contact. Each area presents a
specific linear relationship and the difference of the slopes expresses the different
contribution of the collateral ligaments in the situations where only one or both condyles
are in contact.
Based on these measurements, the varus and valgus weights causing a condyle
lift-off were determined to compute the normalized imbalance expressed in
equation (6.9). By definition, a positive/negative value is related to a lateral/medial imbalance. The normalized imbalance based on the measurement
of contact forces or varus-valgus moments was computed in the same way.
The three approaches to assess the knee stability gave consistent diagnosis for
the majority of the specimens (Fig.6.10). Taken the weight-based assessment
as a reference (Fig.6.11), the force-based assessment has an average difference
of 0%, thus demonstrating the expected equivalence of the two approaches.
6.3. IN-SITU EVALUATION
71
However, the moment-based assessment shows a tendency for lateral imbalance. Even though the average difference was small (6%), large differences
were found in some cases, such as in the third knee. Similar results were
obtained for the measurements performed in 90◦ flexion but with an average difference of imbalance of -4% and 7% respectively for the force-based
and moment-based assessments. The statistical significance, which was again
determined with a sign test for paired samples, was achieved at 90◦ flexion
(p=0.03), but not in full extension (p=0.38).
Figure 6.10: Comparison of imbalance assessment
Assessment of the relative ligament imbalance based on three different parameters: 1.
the varus or valgus weights causing a condyle lift-off, 2. the contact forces and 3. the
varus-valgus moments. The diagnosis given by the three methods were consistent.
72
CHAPTER 6. IN-VITRO STUDY
Figure 6.11: Difference of imbalance
The weight-based approach, which corresponds to the current surgical approach, is taken
as a reference. On average, the force-based approach was equivalent (0%) while the
moment-based approach showed a slight lateral imbalance (6%).
6.3. IN-SITU EVALUATION
73
Finally, the minor and major medial ligament releases reduced the medial
contact force in full extension by 20% and 46% on average (Fig.6.12). The
large standard deviations, 19% and 25%, demonstrated the high variability
of the biomechanical effect of a ligament release among the specimens. The
lateral contact force was just slightly influenced by the medial ligament releases (Fig.6.13), since an average increase of 9%, which is only one fifth
of the reduction on the medial side, was measured. For all specimens, the
variation of the varus-valgus angle was below 0.2◦ , which is not clinically
relevant. This indicates that the ligament release did not substantially modify the tibiofemoral mechanical axis. Finally, the effect of ligament releases
varied strongly along knee flexion, being less relevant at 30◦ and 60◦ than in
full extension or 90◦ flexion (Fig.6.14).
Figure 6.12: Medial contact force reduction
Relative reduction of the medial contact forces following a minor and a major medial
collateral ligament release. The grey and black horizontal lines show the average force
reduction due to a minor and a major release respectively.
74
CHAPTER 6. IN-VITRO STUDY
Figure 6.13: Lateral contact force increase
With an average increase (9%) equivalent to a fifth of the medial force reduction (46%),
the influence of a medial ligament release on the lateral contact force was minor.
Figure 6.14: Effect of ligament release throughout flexion
The release was less effective at 30◦ and 60◦ flexion than in full extension or 90◦ flexion.
The black horizontal lines correspond to the average values at the different positions.
6.3. IN-SITU EVALUATION
6.3.3
75
Discussion
The performance and the clinical advantages of the force-sensing device for
improved ligament balancing procedure in TKA was evaluated with six cadaver knees and four different experiments: compression loading to validate
the device measurements, patella loading to demonstrate the advantage of
keeping the patella in its anatomical place during the measurement, varusvalgus loading to compare the device measurements to the current surgical
approach and finally ligament releasing to quantify its biomechanical effect
in terms of forces.
The very good agreement between applied and measured tibiofemoral contact forces during the compression loading experiment proved the accuracy
and reliability of the in-situ device measurements.
The advantage of having the patella in its anatomical place during the measurement was shown by the significant influence of the patellar eversion on
the mediolateral distribution of the condyle contact forces. One fourth of
the patellar load was shifted to the lateral compartment with a patellar eversion. Although the influence of patellar eversion on the mediolateral force
distribution is intuitive, it is the first time according to the authors’ knowledge that the effect is quantified in terms of forces. Only one recent study
[61] compared the influence of the patellar eversion and subluxation to the
physiological situation in terms of angular variation. With a given interarticular load of 150N for the medial and lateral side, the patellar eversion
increased the leg axis by 2.9◦ valgus. Although a quantitative comparison
to the present study is not possible, the measured effects are qualitatively
consistent. Finally, the fact that the patella in its anatomical place already
influenced the mediolateral distribution of the contact forces could be due to
a non-symmetrical contact area between the patella and the femoral trochlea
or due to the medial incision of the knee joint.
The shape of the curves obtained during the varus-valgus loading experiment
can be biomechanically explained. When the joint opens after condyle lift-off,
the lateral or medial collateral ligament bears a relevant part of the applied
load. Since this part is not measured by the device, it therefore appears as
a drop in the slope. The difference of the slopes between the areas 1 and 3
also demonstrates that the lateral and medial ligaments can have different
stiffness. The determination of the weight causing a medial or lateral condyle
lift-off allowed the comparison of the current surgical approach to assess the
knee instability to the approach based on the measurement of the contact
76
CHAPTER 6. IN-VITRO STUDY
forces or varus-valgus moments. Overall, the three methods gave consistent
results. Weight-based imbalance assessment was equivalent to force-based,
as expected by the simplified two-dimensional model. Moment-based imbalance assessment, which is assumed to be the optimal approach, showed a
tendency of lateral imbalance. This can be anatomically explained by the
fact that the medial condyle is smaller than the lateral [62] and consequently
has its contact point closer to the center of the joint. It should also be noted
that this cadaver model does not take into account any arthritic deformities,
which knees selected for TKA would have. Bone deformities can significantly
shift the condyle contact points and thereby further increase the difference
between the force-based and moment-based imbalance assessment. In such
cases, measuring not only the contact forces but also the varus-valgus moments is an undeniable advantage.
On average, the minor and major medial collateral ligament releases substantially reduced the medial contact force (20% and 46% respectively). The
large variation among the specimens illustrates the difficulty of ligament release. An intraoperative force monitoring during this delicate surgical action
could provide further support to ensure an accurate, patient-specific adjustment of the ligament tensions. The increase of the lateral force after the
major medial ligament release was only a fifth of the decrease on the medial side. Consequently, in the case of a small ligament imbalance requiring
only a minor force reduction, the effect of the ligament release on the opposite side of the surgical action can be neglected. The ligament releases had
also negligible effect on the tibiofemoral alignment. As ligament release can
be considered as a change of the ligament stiffness without modification of
the ligament length, the medial and lateral knee gaps, and consequently the
tibiofemoral alignment, are not affected. It is in opposition to the gap-based
approach where the contact forces are kept constant with a distraction device
such as in the studies reported by Krackow et al. [63], Mihalko et al. [64]
or Baldini et al. [65]. In these cases, diminishing the ligament stiffness with
a ligament release alters the tibiofemoral gap due to constrain on the force
amplitude. Both methods, force-based and gap-based, are conceptually different. While the former measures directly the contact forces determinant for
the component wear, the latter is limited by the complex force-displacement
relationship of ligaments, which moreover is not necessarily identical on the
medial and lateral side. A well balanced distribution of medial and lateral
contact forces avoids overload of one compartment and thus premature wear.
Finally, a variation of the effect of ligament releases along knee flexion was
observed. A different arrangement of the ligament fibers in the different positions could explain this variation. This again exemplifies the complexity of
6.3. IN-SITU EVALUATION
77
ligament balancing and the importance of an intraoperative force monitoring.
In conclusion, the device worked correctly under realistic conditions of use.
In addition to the accurate imbalance assessment based on the measurement
of forces and moments, important clinical advantages, such as the possibility
to keep the patella in its anatomical place during the measurement or the
real-time force monitoring during the delicate phase of ligament release, were
demonstrated. The proposed device has thus shown potential to improve the
ligament balancing procedure and the lifetime of TKA.
78
CHAPTER 6. IN-VITRO STUDY
Chapter 7
Clinical trials
7.1
Safety requirements
Before testing the device in-vivo, a risk analysis must be performed. Three
kinds of risks can be identified:
1. Mechanical risks
• Damage to healthy tissues
• Rupture of the device
2. Chemical risks
• Contamination with toxic substances
• Infection
3. Electrical risks
• Electromagnetic disturbances
• Electric shocks
Since the shape of the device was designed to follow the contours of the tibial
plateau, surrounding soft tissue is expected to be unaffected by insertion or
use of the device. Furthermore, the plasticity test showed that the device
stays in the elastic range with forces up to 1’500N. It is therefore expected
that the force required to break the device is well over the maximum in-vivo
load, thus making an in-situ rupture of the device impossible. Consequently,
complications due to mechanical problems are very unlikely.
79
80
CHAPTER 7. CLINICAL TRIALS
All the metallic parts constituting the device are made of biocompatible stainless steel or titanium. The wires have an insulation of teflon, a chemically
inert material. All the connectors used are certified for medical applications.
Therefore, the only possibility of chemical contamination comes from the
exposed circuitry, piezoresistive sensors and soldering tabs. However, the
parylene coating ensures a full chemical barrier and prevents toxic exposure
to these parts. Finally, a standard sterilization procedure is adopted to minimize risks of infection.
With a power supply of 5V DC, the device should not disturb any other
surgical device through electromagnetic interferences. Nevertheless, particular attention must be paid to potential electric shocks. The device has to
comply with the general requirements of the standard for medical electrical
equipment [66]. The two most important requirements are: a) a galvanic
separation that prevents direct connection between the electric network and
the patient and b) a patient leakage current that must not exceed 10µA in
normal condition and 50µA in single fault condition. Although the parylene
coating provides a good electric isolation (3500V DC and 2500V AC), a special signal conditioning unit has been produced to further ensure the patient
safety in a fault condition (Fig.7.1).
Figure 7.1: Custom signal conditioning unit
The principle for the electric isolation of the patient is schematically explained in Fig.7.2. The signal conditioning unit is powered by a power sup-
7.1. SAFETY REQUIREMENTS
81
ply certified to provide a galvanic separation and to ensure a patient leakage
current lower than 10µA. A standard industrial amplifier for strain gauge
applications is then used to power the Wheatstone bridge and to amplify its
output. Finally, the electrical signal goes through an optical decoupling that
prevents uncontrolled currents coming from the computer from harming the
patient. The main component of this electronic circuit, which is shown in
details in Fig.7.3, is an optocoupler. This device has two diodes ; one that
emits light to convert the input voltage into a luminous flux and a second
that receives this light and converts it back into a voltage output. This way,
the information contained in the electrical signal is transmitted without any
electrical contact between the patient and the data acquisition computer.
Medical
Power
Supply
Sensor
Industrial
Amplifier
Optocoupler
DAQ &
Computer
Figure 7.2: Patient isolation principle
The medical power supply complies with the medical standard and
therefore can be in direct contact with the patient. The optical decoupling
prevents uncontrolled external current from harming the patient.
Figure 7.3: Electronic diagram of the optical decoupling
CHAPTER 7. CLINICAL TRIALS
82
7.2
Standard approach vs force-sensing device
Two clinical trials were carried out both to evaluate the device performance
in a surgical environment and to compare the device-assisted to the standard approaches under real conditions of use. To realize these objectives,
two sets of measurements in full extension and in 90◦ flexion were carried
out, the first before the femoral cuts were performed and the second after
the trial femoral component was placed. After the device insertion, spacers
of different thicknesses were introduced to balance the ligament according to
the device measurements (Fig.7.4). Then, the device was removed and the
surgery proceeded in a standard way. The thickness of the resected condyles
was measured for the distal and posterior cuts. Once the trial femoral component was in place, the device was introduced a second time. Spacers were
used again to assess the remaining knee imbalance according to the device
measurements. The femoral cuts planned by the device measurements, the
femoral cuts performed on the basis of standard instrumentation as well as
the final imbalance assessment were then compared.
Balanced knee
Femoral cuts
Difference
Final imbalance
Patient A
Extension Flexion
3mm
4mm
3.5mm
1mm
-0.5mm
3mm
-1mm
2mm
Patient B
Extension Flexion
6mm
3mm
6mm
2mm
0mm
1mm
0mm
0mm
Table 7.1: Mediolateral difference of the knee gaps
A positive, negative sign corresponds to the medial, lateral side respectively.
The results are summarized in table 7.1. According to the device measurements, the knee of patient A could be balanced with a mediolateral difference
in the knee gaps of 3mm in extension and 4mm in flexion. The femoral cuts
performed with a standard approach showed a gap difference of 3.5mm in
extension and 1mm in flexion. Therefore, the device measurements and the
standard approach agreed in extension but not in flexion. However, the
surgeon also estimated at that point of the surgery that the knee was not
completely balanced and that a ligament release was required. The knee
of patient B could be balanced with a mediolateral knee gap difference of
6mm in extension and 3mm in flexion. The femoral cuts had a gap difference
of 6mm in extension and 2mm in flexion, showing a complete agreement
7.2. STANDARD APPROACH VS FORCE-SENSING DEVICE
(a) Overview of the operating room
(b) Introduction of spacers
Figure 7.4: Clinical trial
Spacers are introduced to balance the knee according to the device measurements
83
84
CHAPTER 7. CLINICAL TRIALS
between the device-assisted and the standard approaches. The imbalance
assessment with the femoral component in place resulted in values similar
to the difference between the device-planned femoral cuts and the femoral
cuts effectively performed, thus demonstrating the consistency of the device
measurements throughout the surgery.
In addition to these measurements, five dynamic evaluations were performed
during knee flexion before the femoral resection. Fig.7.5 shows the variation
in medial and lateral forces for patient A as the device spacers were set to
balance the knee at 90◦ flexion. The huge difference of force amplitude in
flexion and in extension, and thereby the huge difference in balance, is in
agreement with the well-known fact that tibiofemoral gaps ensuring a stable
knee are not necessarily the same in flexion and in extension.
Figure 7.5: Flexion-extension of the knee
In conclusion, these in-vivo trials demonstrated that the device measurements are possible, meaningful and consistent with the surgeon’s perception
in a clinical environment.
Chapter 8
Unicompartmental knee
arthroplasty
8.1
Surgical procedure
Unicompartmental Knee Arthroplasty (UKA) is a surgical procedure which
consists in replacing either the medial or lateral knee compartment (Fig.8.1).
This procedure is indicated when significant degenerative changes exist in
only one of the compartments and when the cruciate ligaments are intact.
Candidate patients should not be obese, should have good preoperative range
of motion (90◦ flexion), and a deformity below 15◦ [67]. These strict selection criteria are responsible for the result that only 5-7% of arthritic knee
joints are treated with UKA. The theoretical advantages of UKA compared
to TKA are a preservation of the intact tissue and bone, a reduction in operating time as well as a better range of motion and improved gait.
UKA was introduced 30 years ago, but frequent and early failures at that
time made the treatment controversial. TKA with its encouraging long-term
success became the standard procedure. However, in the past few years, a
resurgence of interest in the UKA has occurred, particularly with the introduction of minimally invasive techniques. With improved surgical procedures
and optimized prostheses, the long-term results with current UKA procedures
are now comparable to TKA ones, even though the demanding patient selection may influence the lifetime [68, 69, 70]. Moreover, a knee joint having
received a unicompartmental implant can later undergo a TKA, with minimal loss of implant-supporting subchondral bone. Thus, at the point of a
TKA, the UKA patient has gained the intervening time over an initial TKA
patient.
85
86
CHAPTER 8. UNICOMPARTMENTAL KNEE ARTHROPLASTY
(a) Prosthetic components
(b) Postoperative X-ray
Figure 8.1: Unicompartmental Knee Arthroplasty
The Oxford Knee from Biomet Europe, Dordrecht, The Netherlands
Aside from the common complications from arthroplasty, the main problem
with UKA is the potential for over or undercorrection of the mechanical axis.
In the case of overcorrection, excessive loads on the second knee compartment lead to an accelerated degeneration. On the other hand, undercorrection gives abnormal laxity, inducing component loosening or failure. The
mechanical axis correction and the joint stability is carried out by inserting
thicker or thinner polyethylene meniscal bearing [71, 72]. Ligament release
is usually not performed or is minor. In order to avoid overcorrection, which
has consequences on the healthy compartment, an undercorrection of the
mechanical axis of 2-3◦ is usually performed. For example, Thornhill [71]
recommends to leave some medial tibial opening in extension in the case of
medial compartment osteoarthritis. Although this practise is tolerable, it is
not optimal. According to Emerson et al. [73], the restoration of normal
soft-tissue tension by the insertion of the appropriately sized implant can
consistently restore axial alignment within the physiological range. Quantitative measurement of the tibiofemoral condyle contact forces here could help
the surgeon to assess the ligamentous balance and consequently to determine
the optimal implant size.
8.2. SOFT-TISSUE BALANCING ASSISTANCE FOR UKA
8.2
8.2.1
87
Soft-tissue balancing assistance for UKA
Concept
Since the contralateral knee compartment is not accessible during the surgery,
only one sensitive plate can be used. This implies that only half of the
parameters required to provide a quantitative evaluation of the knee balance
can be measured. Applying and measuring external varus-valgus loads on
the leg in addition to the one plate measurements can compensate for the
missing information on the healthy side.
FML
FLL
y
x
FMC
FLC
d
Fext
Figure 8.2: Knee joint experiencing external varus-valgus moments
The measurement principle is based on the same simplified planar model of
the knee joint presented in section 3.1, except that an external force Fext is
applied at the distal part of the tibia at a distance d (Fig.8.2). The forces
Fi , i={M L, M C, LC, LL} are the medial ligament, the medial contact, the
lateral contact and the lateral ligament forces. To satisfy the equilibrium
condition, the sum of the moments must be zero.
dFext + xM L FM L − xM C FM C + xLC FLC − xLL FLL = 0 ,
(8.1)
88
CHAPTER 8. UNICOMPARTMENTAL KNEE ARTHROPLASTY
where xi is the lever arm of the force Fi , i={M L, M C, LC, LL}. By
renaming and regrouping the amplitude of the different moments, equation
(8.1) can be rewritten as:
Mlig − MM + ML + Mext = 0 ,
(8.2)
where Mlig is the net varus-valgus moment of the collateral ligaments and
Mi , i={M , L, ext}, are the moment amplitudes of the medial, lateral and
external forces respectively. The amplitude of the contact moments MM ,
ML obviously depend on the external moment Mext . However, if bones are
considered as rigid bodies and ligament as springs, the ligament forces and
therefore Mlig can be assumed constant as long as both condyles are in contact with the tibia. The tension in a spring-ligament would vary only when
the joint starts to open, i.e. when one condyle lifts off. Therefore, the net
varus-valgus moment of the ligaments is given by:
Mlig = MM − ML − Mext
0
0 ≤ Mext ≤ Mext
,
(8.3)
0
corresponds to the moment creating a condyle lift-off. Since
where Mext
this last equation is verifiedvalid for all the values of Mext comprised in the
specified range, it is true for the two border values:
Mlig = MM − ML
0
Mlig = MM − Mext
for Mext = 0
0
for Mext = Mext
.
(8.4)
(8.5)
Equation (8.4) shows that Mlig is equivalent to Mnet , the net varus-valgus
moment of the contact forces that characterizes the knee balance (c.f. section
3.1) and equation (8.5) shows that it can be computed by measuring the
medial and the external moments at the time of condyle lift-off:
. 0
− Mext
.
(8.6)
Mnet = MM 0
. Mext =Mext
In practise, the medial moment MM is measured by the sensitive plate and
the external moment Mext can be computed from the measurement of the
external force amplitude with a dynamometer and the lever arm with a ruler.
The experimental issue is then to precisely determine the moment of condyle
lift-off without seeing the condyle. According to equation (8.2), a linear
relationship exists between the contact moment and the external varus-valgus
moment. However, the proportionality factors are not the same before and
after condyle lift-off since Mlig is constant and ML non-zero before, whereas
0
Mlig varies and ML is zero after lift-off. The specific external moment Mext
at the moment of lift-off can thus be determined by identifying the slope
discontinuity in the curve MM (Mext ).
8.2. SOFT-TISSUE BALANCING ASSISTANCE FOR UKA
8.2.2
89
In-vitro feasibility study
The delicate point of the proposed method resides in the hypothesis that Mlig ,
the net varus-valgus moment of the collateral ligaments, does not vary before
condyle lift-off. In practise, the knee joint is more complex than rigid bodies
linked with springs. For instance, the femoral cartilage can be compressed
and behaves as a spring-like structure or the relative position between the
femur and tibia can slightly vary during loading, thus altering the ligament
tension. The goal of this section is therefore to quantify the deviation of the
model from the reality in order to estimate if the proposed approach could
be used clinically.
If Mlig is constant, a partial derivative of equation (8.3) gives
∂
(MM − ML ) = 1 .
∂Mext
(8.7)
Consequently, plotting the net varus-valgus moment MM − ML in function
of the external moment Mext should show a linear relationship with a slope
of 1. To experimentally verify that point, the data acquired during the
varus-valgus loading experiment of the in-vitro study (c.f. section 6.3) were
used. For each specimen, the relationship was, as expected, highly linear
(0.99≤ r2 ≤1.00), such as in the example showed in Fig.8.3. However, the
measured slopes ranged from 0.63 to 0.78, the average being 0.69 instead of
1 (Table 8.1). This implies a relative error of the model of 30%, which is
obviously not acceptable.
slope
pilot
0.78
knee 1
0.72
knee 2
0.61
knee 3
0.74
knee 4
0.66
knee 5
0.69
knee 6
0.63
Table 8.1: Slope of the ligament moment vs applied moment
The hypothesis of constant ligament forces before condyle lift-off is therefore too strong. In order to improve the proposed approach, the variation
of the net varus-valgus moment of the ligaments Mlig as a function of the
external moment Mext must be taken into account. An estimate of this variation may be derivable from an intraoperative measurement of the change
of the lengths LM , LL of the medial and lateral ligaments with the help of
a navigation system. Knowing this length variation, the force and thereby
the moment variation can be estimated by using a generic or patient-specific
ligament stiffness (KM , KL ). The latter can be determined by comparing
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CHAPTER 8. UNICOMPARTMENTAL KNEE ARTHROPLASTY
Figure 8.3: Comparison of the contact moments and external moments
contact forces measured by the device and ligament lengths measured by
the navigation system in different external loading conditions. With these
parameters, the varation of the ligament moment can be computed as follows:
. . −
M
= xM L KM ∆LM − xLL KL ∆LL ;
(8.8)
Mlig lig 0
. Mext =Mext
. Mext =0
and equation (8.6) can thus be corrected.
. 0
Mnet = MM − Mext
− (xM L KM ∆LM − xLL KL ∆LL )
0
. Mext =Mext
(8.9)
In conclusion, substituting the missing information of the healthy side by
applying known varus-valgus moments is not sufficient to provide precise
stability assessment. Additional measurements, such as the variation of the
ligament length, are necessary.
Chapter 9
Conclusion and perspectives
This thesis addressed the issue of the measurement of musculoskeletal forces
during orthopaedic surgeries through the development of a force-sensing device for ligament balancing in Total Knee Arthroplasty (TKA). In addition
to geometrical parameters given by the standard orthopaedic instrumentation, the measurement of forces involved at the time of surgery can help in
improving the placement of implants and/or the adjustment of surrounding
soft-tissues to ensure a consistent procedure. During TKA, a good ligament
balance must be achieved to ensure a stable and functional prosthetic knee
joint. Internal joint forces and moments are therefore of major importance
but are nowadays only qualitatively assessed with manipulation or basic instrumentation.
In a first step, three possible designs for a force-sensing device for knee arthroplasty were proposed and studied using finite element analysis. The optimal
design consists of two sensitive plates, one for each condyle, a tibial base
plate, which is fixed by pins, and a set of lateral and medial spacers, which
allow the device thickness to be adapted to the patient-specific tibiofemoral
gaps. The entire device fits inside the knee joint after the initial tibial cut
with the patella in its anatomical place. The ligament balance assessment
can be carried out at the beginning of the surgery, thus offering the possibility to make a better plan for the femoral cuts and the femoral component
rotation. Thanks to the top spacer system, additional spacers having the top
surface congruent to femoral implants can be easily used to allow measurements and ligament adjustments with the trial components in place. Thus,
the main stability assessment made at the beginning of the surgery enables
better planning of the femoral cuts, whereas the second at the end of the
surgery allows fine-tuning of the ligament balance and correcting eventual
deviations from the plan. Each sensitive plate contains three deformable
91
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CHAPTER 9. CONCLUSION AND PERSPECTIVES
bridges instrumented with thick-film piezoresistive sensors. This three-point
measurement allows determining the amplitude and location of the load applied on a sensitive plate. With these measurements, the net varus-valgus
moment, which has been identified as the biomechanical parameter characterizing the knee balance, can be computed. Laboratory experiments showed
that the device has an 0.5% full scale accuracy in the range 0-500N and a
1.6N maximal measurement error in the range 0-100N, the expected active
range of use. Thus, the accuracy is adequate and the measurement principle
and the device design validated.
In a second step, an in-vitro study demonstrated the proper in-situ functioning of the novel force-sensing device as well as its clinical advantages.
For example, patellar eversion, necessary with standard approaches but not
with the proposed device, had a significant influence on the mediolateral distribution of the contact forces: one fourth of the patellar load was shifted
to the lateral side. Besides the validation of the device design, this in-vitro
study also addressed two biomechanical issues. The first is the absence of
standard interpretation in biomechanical terms of what surgeons intuitively
call ligament balancing. Contact pressure, contact forces, tibiofemoral gaps,
angular asymmetry, etc., are parameters interchangeably used in literature
to describe the ligament balance. To identify which biomechanical parameter
the surgeon intraoperatively assesses, the current surgical approach (difference of varus and valgus weights generating a condyle lift-off) was compared
theoretically and experimentally to the measurement of contact forces or
moments. The weight-based method was similar to the force-based, while
the moment-based, proposed as the optimal from the biomechanical point
of view, showed a slight lateral imbalance. Surgeons must then be aware
that knee stability before and after the insertion of the femoral component
may differ even if the ligament forces do not. Instrumentation that bases the
ligament imbalance assessment on the measurement of contact forces and
moments should therefore be used during the planning of the femoral cuts.
The second biomechanical issue is the lack or poor documentation of the
effect of ligament release, one of the most used surgical action to correct imbalance, in terms of knee joint forces. Medial contact forces measured after
minor and major medial collateral ligament releases were reduced by 20%
and 46% in average. The high standard deviations, 19% and 25% respectively, demonstrated the high variability among specimens and therefore the
need of an intraoperative monitoring to ensure a patient-specific adjustment
of ligament tensions.
93
In a final step, two in-vivo trials confirmed that the device measurements
are possible, meaningful and consistent with the surgeon’s perception in a
clinical environment.
The novel force-sensing device has therefore an appropriate design and performs correctly. In addition to the accurate imbalance assessment based on
the measurement of forces and moments, important clinical advantages, such
as the possibility to keep the patella in its anatomical place during the measurement or the real-time force monitoring in the delicate phase of ligament
release, were demonstrated. The proposed device has thus shown potential
to improve the ligament balancing procedure and the lifetime of TKA.
In order to further enhance the device, two ergonomic changes could be implemented. Firstly, the fixation mechanism serving to extend the sensitive
area could be replaced by a hinge mechanism at the extremity of the bridge
pillars, which would extend the sensitive area to the whole plate while suppressing protuberant parts. Secondly, the data transfer to the computer
could be improved by using a multiplexing or a telemetry to reduce or avoid
wires. A prototypical telemetric system based on the principle of near-field
magnetic induction coupling, commonly used in RFID (Radio Frequency
IDentification) applications, was designed and tested by a research partner
[47]. The technical feasibility was demonstrated but further work is needed
to reduce the size of the electronics to be able to integrate it in the device. In
addition to these ergonomic improvements, the functionality of the new instrument can be extended by combining the device with a navigation system.
Measuring simultaneously geometrical parameters, such as angles, lengths,
axes, and mechanical such as forces and moments enables the use of complex computational knee models, which can act as assistive expert systems.
The advantages that such a tool can offer was already perceived during the
feasibility study of the adaptation of the force-sensing device for unicompartmental knee arthroplasty. Complete assistive expert systems, which intraoperatively provide an accurate measurement of geometrical and mechanical
parameters, a quantitative biomechanical interpretation and finally a precise
guidance to achieve the plan will undeniably become an essential tool in the
next generation of orthopaedic instrumentation.
The first in-vivo trials, which concluded the experimental phase of the thesis, correspond to the starting point of large clinical studies. Thanks to the
developed force-sensing device several important biomechanical and clinical
issues can be addressed, such as the accuracy and repeatability of the surgeon’s performance in soft tissue balancing ; the correlation between intra-
94
CHAPTER 9. CONCLUSION AND PERSPECTIVES
operative ligament imbalance, postoperative knee laxity and postoperative
complications ; the lifetime of TKA performed with an assistive expert system compared to standard instrumentation. Up to now, all these important
questions could not be studied quantitatively. The new proposed tool has
therefore a promising future in research, too.
As has been seen through the development of this force-sensing device for
knee arthroplasty, intraoperative measurements of musculoskeletal forces is
of major importance and can bring useful help during orthopaedic surgeries.
Precise and objective assessment of biomechanical parameters is a valuable
complement to the surgeon’s perception and the combination of smart surgical instrumentation and human-specific performances should definitely lead
to a significant benefit for the patient.
Appendix A
Some basics of solid mechanics
The purpose of this section is not to give an exhaustive course on solid
mechanics, but simply to review and introduce the fundamental concepts
used in this thesis. More details on solid mechanics can be found in [10].
A.1
Elastic deformation
Two fundamental concepts in mechanics of materials are stress and strain.
Stress is the intensity of a force per unit of area and is denoted by σ. Assuming that the stresses are uniformly distributed over a cross section of a
body (Fig.A.1), the stress amplitude is expressed by
P
,
(A.1)
A
where P is the axial force and A the area. By definition, stress is positive
when the specimen is tensed and negative when it is compressed.
σ=
Figure A.1: Definition of stress
Stress σ is the intensity of a force P per unit of area A (picture taken from [10])
A straight bar becomes longer in axial tension and shorter in axial compression. The resulting strain is denoted by and is defined as the ratio between
95
96
APPENDIX A. SOME BASICS OF SOLID MECHANICS
this length change (∆L) and the original length (L),
=
∆L
.
L
(A.2)
As for the stress, the strain is positive when the bar becomes longer and
negative when it becomes shorter.
The relationship between stress and stain is empirical and based on the socalled stress-strain diagram, whose typical example is that of steel (Fig.A.2).
In the first part of the diagram, from O to A, the relationship is linear. This
area is called the elasticity range of the material and the slope is the modulus of elasticity or Young’s modulus. The point A is the elasticity limit.
Beyond this point, the stress-strain becomes less steep until, at point B, the
curve becomes horizontal. This phenomenon is known as yielding of the
material and point B is called the yield point. In the region from B to C,
the material becomes perfectly plastic, which means that it deforms without
an increase of the applied load. After undergoing the large strains that occur during yielding in the region BC, the material begins to strain harden.
During strain hardening, the material undergoes changes in its crystalline
structure, resulting in increased resistance of the material to further deformation. Elongation of the test specimen in this area requires an increase in
the tensile load, which reaches its maximum value, the ultimate stress, at the
point D. Further stretching of the bar is actually accompanied by a reduction
in the load and fracture finally occurs at point E.
The relationship between stress and strain in the elastic range for a bar in
simple tension or compression can be expressed as
σ = E ,
(A.3)
where E designates the Young’s modulus. This formula is known as Hooke’s
law.
In addition to elongation along the axis of loading, the bar reduces its section
to keep the volume constant, thus generating lateral strain . This lateral
strain is proportional to the axial strain at the same point. The dimensionless ratio ν between these two kinds of strains is a property of the material
called Poisson’s ratio, which can be expressed as
ν=− .
(A.4)
A.1. ELASTIC DEFORMATION
97
Figure A.2: Stress-strain diagram
Typical structural steel in tension (picture taken from [10])
Taking the lateral strain into account, the triaxial Hooke’s law can be written
as follows:
1
(σ1 − νσ2 − νσ3 )
E
1
=
(σ2 − νσ1 − νσ3 )
E
1
(σ3 − νσ1 − νσ2 ) .
=
E
1 =
2
3
(A.5)
In addition to axial loads, tangential loads can act on a specimen’s surface.
These loads generate shear stresses, which are denoted by τ . Contrary to axial stress which tends to modify the length of a specimen, shear stress tends
to change its shape. The corresponding strain is not the relative length variation anymore, but the angle of distortion γ (Fig.A.3).
The shear stress-strain diagram is similar in shape to the tension stress-strain
diagram, although it differs in magnitude. A linear relationship, which is
called the Hooke’s law in shear, also exists close to the origin.
τ = Gγ ,
where G is the shear modulus.
(A.6)
98
APPENDIX A. SOME BASICS OF SOLID MECHANICS
Figure A.3: Shear stress
Element of material subjected to shearing stresses and strains, before and after
deformation (picture taken from [10])
Apparently, 12 shear stress components (2 per face for 6 faces) are required
to completely describe the state of a general three-dimensional stress element. However, stresses occurring at opposing faces have opposite signs,
thus reducing the number of significant components to 6. Moreover, in order
to satisfy static equilibrium, the shear stress components are related in the
following way:
τyz = τzy
τzx = τxz ,
(A.7)
τxy = τyx
where the first subscript is the coordinate normal to the element face and the
second designates the axis parallel to the shear-stress component. Therefore,
only 3 components are significant, or, in other words, independent. This
leads to use the following three equations for a three-dimensional case of
pure shear:
τxy = Gγxy
τyz = Gγyz
τzx = Gγzx .
(A.8)
Although the normal and shear stresses were discussed separately, both can
simultaneously occur in a general load state. The set of equations (A.5)
and (A.8) must therefore be used. Considering such a general case, it is
possible to demonstrate that the Young’s modulus, the shear modulus and
the Poisson’s ratio are related to each other by
G=
E
.
2(1 + ν)
(A.9)
Finally, note that all previous considerations are only valid for homogenous
and isotropic material.
A.2. STRESSES IN BEAMS
A.2
99
Stresses in beams
An important and widely used mechanical structure in the domain of forcesensing devices is the bending beam. To establish the stress formula for
bending beams, let’s consider the Fig.A.4, which presents the side view and
the cross section of a beam as well as its deformation resulting from bending
moments.
Figure A.4: Deformation of beam in pure bending
a) side view, b) cross section, c) deformed beam (picture taken from [10])
When loads are applied to a beam, its longitudinal axis is deformed into a
curve. The curvature (κ) is by definition the inverse of the radius of curvature
(ρ), that is
1
(A.10)
κ= .
ρ
100
APPENDIX A. SOME BASICS OF SOLID MECHANICS
The neutral axis, the axis along which there is no stress, is represented by
a dashed line. Since the distance dx between the planes containing cross
sections mn and pq is part of this neutral axis which undergoes no strain, it
remains the same before and after deformation, thus allowing us to write
ρdθ = dx ,
(A.11)
giving
dθ
.
(A.12)
dx
On the other hand, a line ef at a distance y from the neutral axis becomes
shorter or longer. Its original length is clearly dx and its length after deformation is
y
(A.13)
(ρ − y)dθ = dx − dx .
ρ
The corresponding strain is therefore
κ=
x =
(dx − yρ dx) − dx
dx
y
= − = −κρ ,
ρ
(A.14)
and stress
σx = Ex = −Eκy .
(A.15)
To express the curvature in mechanical terms, the second equation of equilibrium, which expresses the fact that the sum of the moments should be zero,
has to be used. Considering a small part of the beam, the element of force
σx dA acting on an element dA is in the positive direction of the x axis when
σx is positive and inversely. An infinitesimal moment is therefore generated,
dM = −σx ydA ,
thus giving by integration
M = − σx ydA = κE
y 2 dA = κEI ,
A
(A.16)
(A.17)
A
where I is the moment of inertia.
I=
y 2 dA
(A.18)
A
The curvature can hence be expressed by
κ=
1
M
=
.
ρ
EI
(A.19)
A.2. STRESSES IN BEAMS
101
Finally, by combining equations (A.15) and (A.19), the flexure formula is
obtained:
My
σx = −
.
(A.20)
I
This general expression gives the stress for a given cross-section in a specific
plane, but designers are more interested in knowing the maximal stresses.
These obviously occur at the top and bottom surface of the beam, when y
is maximal. In order to give an analytical expression, two specific cases, a
rectangular and a circular beam, are now reviewed.
1. Let’s consider a rectangular beam with a width b and a height h. If
a force is acting in its center, the maximal possible value for y is h/2.
After integration, the moment of inertia is
I=
bh3
,
12
(A.21)
and the maximal stress amplitude for a rectangular beam is
σx =
6M
bh2
(A.22)
2. Let’s consider a circular beam with a diameter d and a force acting
in its center. The maximal value for y is d/2. After integration, the
moment of inertia is
πd4
I=
.
(A.23)
64
The maximal stress amplitude for a circular beam is
σx =
32M
πd3
(A.24)
Finally, note that this analysis is valid only for pure bending. Nonuniform
bending, which corresponds to bending moment that is not constant along
the beam, will produce distortion of the cross section. This distortion has
not been taken into account in the previous development. However, detailed
investigations show that the normal stresses calculated from the flexure formula are not significantly altered by the shear stresses. Thus, the theory of
pure bending for calculating normal stresses in beams subjected to nonuniform bending can be justifiably used.
It has also to be reminded that this analysis does not take into account
eventual stress concentrations, making the theory inaccurate near the support
of the beam or close to a concentrated load.
102
APPENDIX A. SOME BASICS OF SOLID MECHANICS
Appendix B
Contact pressure and stresses
To evaluate if yielding of a body being in contact with other mechanical parts
will occur, a two-step calculation has to be performed:
1. Assess the maximal contact pressure (B.1)
2. Determine if this maximal pressure leads to plastic yielding (B.2)
B.1
Hertzian theory
This typical contact stress problem was solved by Hertz in 1881 for the first
time. Even if the Hertzian theory is more than hundred years old, it is still
largely used and has been numerous times validated.
The mathematical description that follows is from [74]. A more general approach, which leads to the same final result, can be found in [75].
Let’s consider two bodies, which have spherical surfaces of radii R1 , R2 at
the contact point (Fig.B.1). Without pressure between the bodies, the contact point is located in O. The distances from the plane tangent at O of
points such as M, N , at a very small distance r from the axes z1 , z2 , can be
represented with sufficient accuracy by the formula
z1 = R12 −
r2
R12 − r2 ∼
=
2R1
(B.1)
and the respective distance between these points is
z1 + z2 =
r2 (R1 + R2 )
.
2R1 R2
103
(B.2)
104
APPENDIX B. CONTACT PRESSURE AND STRESSES
Figure B.1: Two spheres in contact
(picture taken from [74])
In the particular case of contact between a plane and a sphere (Fig.B.2),
1/R1 = 0 and the mutual distance becomes
r2
z1 + z2 =
.
2R2
(B.3)
In the case of contact between a ball and a spherical seat (Fig.B.2), R1 is
negative and the mutual distance is
z2 − z1 =
r2 (R1 − R2 )
.
2R1 R2
(B.4)
Figure B.2: Different contacts
a) sphere on a plane, b) sphere in spherical socket (picture taken from [74])
Applying a load F on the spheres obviously leads to deformation. This
gives a compliance δ corresponding to the movement in the vertical direction
of points at a distance r from the loading point, such as M, N . If the
B.1. HERTZIAN THEORY
105
displacements at these points are w1 , w2 , then, for points inside the contact
area:
(B.5)
(z1 + w1 ) + (z2 + w3 ) = δ .
With (B.2), this last equation can be written as:
w1 + w2 = δ − βr2 ,
where β =
(B.6)
R1 +R2
.
2R1 R2
Assuming that the radii of curvature R1 , R2 are large in comparison to the
radius of the contact surface, the result obtained for semi-infinite bodies in
[74] can be applied: the displacement w1 of a point on the surface of contact
of the lower ball is
1 − ν12
P ds dψ = K1
P ds dψ ,
(B.7)
w1 =
πE
1 =K1
where ν1 , E1 are the Poisson’s and Young’s modulus respectively and P the
pressure. A similar expression can be written for the upper ball. Thus, (B.6)
becomes
P ds dψ = δ − βr2 .
(B.8)
(K1 + K2 )
A satisfying assumption is that the distribution of pressure P over the contact
area is represented by the ordinates of an hemisphere of radius a, constructed
on the surface of contact. If Pmax is the pressure at the center of the contact
area, then
(B.9)
Pmax = ka ,
where k is a constant factor representing the scale factor of our representation
of the pressure distribution. After integration, (B.8) becomes
(K1 + K2 )
π 2 Pmax
(2a2 − r2 ) = δ − βr2 .
4a
(B.10)
Since this last equation has to be fulfilled for any value of r, it has to be
valid for r = 0 and r = a. Therefore, the following relationships exist for
compliance δ and the radius a of the surface of contact:
π2a
2
π2
a = (K1 + K2 )Pmax
.
4β
δ = (K1 + K2 )Pmax
(B.11)
APPENDIX B. CONTACT PRESSURE AND STRESSES
106
The value of the maximal pressure Pmax is obtained by equating the sum
of the pressures over the contact area to the compressive force F . For the
hemispherical pressure distribution, with Pmax /a being the pressure per unit
of ordinates and 2/3πa3 the hemisphere volume, this gives
Pmax 2 3
πa = F ,
a 3
(B.12)
from which
3F
.
(B.13)
2πa2
The maximal pressure is thus 1.5 the average pressure of the contact area.
Pmax =
Finally, combining the expressions (B.11) and (B.13) gives the final result
R1 R2
3π
a = 3
F (K1 + K2 )
4
R1 + R2
9π 2 2
(R1 + R2 )
δ = 3
(B.14)
F (K1 + K2 )2
16
R1 R2
F
(R1 + R2 )2
1 3 6
Pmax =
.
π π 2 (K1 + K2 )2 R12 R22
Note that by taking R1 infinite or negative, the equations are valid for a ball
on a plane or in a socket. For a ball in a spherical seat, this gives:
1
6
F
(R1 − R2 )2
.
Pmax = 3 2
π π (K1 + K2 )2 R12 R22
B.2
Distortion-energy criterion
Although the maximal pressure in the contact area can be calculated, a criteria to evaluate its effect on the material (elastic, plastic deformation or
failure) must be defined. In other words, the correlation between the experienced stress and the yielding point or the ultimate tensile strength of the
material should be determined. Unfortunately there is at present time no
fundamental rationale for such correlation and the use of empirical relationships, which have been widely proved by experiments, is required. One of the
most popular is surely the von Mises or distortion-energy criterion, which is
described below [76].
B.2. DISTORTION-ENERGY CRITERION
107
Postulate
Yielding will occur when the distortion-energy per unit volume equals the
distortion-energy per unit volume in a uniaxial tension specimen stressed to
its yield strength.
The strain energy per unit volume is given by
1
1
1
U = σ1 1 + σ2 2 + σ3 3 ,
2
2
2
(B.15)
where σi , i are the principal stress and strain components. An expression of
the strain energy per unit volume in terms of stress only can be obtained by
using the stress-strain relationships,
1
(σ1 − νσ2 − νσ3 )
E
1
=
(σ2 − νσ1 − νσ3 )
E
1
=
(σ3 − νσ1 − νσ2 ) ,
E
1 =
2
3
(B.16)
thus giving
U=
1 2
σ1 + σ22 + σ32 − 2ν(σ1 σ2 + σ2 σ3 + σ3 σ1 ) .
2E
(B.17)
The principal stress components can be theoretically separated into two different contributions: the hydrostatic and the distortional stresses (Fig.B.3).
By definition, the hydrostatic stress is given by
σh =
σ1 + σ2 + σ3
.
3
(B.18)
On one hand, the hydrostatic stresses cause a change only in volume, not
in shape. A cube gets bigger in tension and smaller in compression, but
remains a cube. On the other hand, distortional stresses act to deform or
distort the material element. There is no change in volume, only in shape.
These stresses try to elongate or compress the material more in one direction
than in another and are responsible for yielding.
108
APPENDIX B. CONTACT PRESSURE AND STRESSES
Figure B.3: Hydrostatic and distortional stresses definition
The distortional strain energy is equal to the difference between the total
strain energy and the hydrostatic strain energy.
Ud = U − Uh
1 2
σ1 + σ22 + σ32 − 2ν(σ1 σ2 + σ2 σ3 + σ3 σ1 )
=
2E
2
3 1 − 2ν σ1 + σ2 + σ3
−
2 E
3
1+ν 2
Ud =
[σ + σ22 + σ32 − σ1 σ2 − σ2 σ3 − σ1 σ3 ]
3E 1
(B.19)
Thus, the distortional strain energy depends only on the effective stress,
ususally called the von Mises stress, defined by
σef f = σ12 + σ22 + σ32 − σ1 σ2 − σ2 σ3 − σ1 σ3 .
(B.20)
In a uniaxial tension test (σ2 = σ3 = 0), this effective stress is equivalent to
the tension stress;
(B.21)
σef f = σ1 .
Therefore, this effective stress is the parameter which should be compared
to the tensile strength of the material to determine if yielding may occur or
not.
B.3
Conclusion
From the two previous sections, the maximal contact pressure an the effective stress that has to be compared to the tensile strength of material can
be computed. However, the link between both parameters still need to be
determined. The maximum stresses of two spherical bodies in contact obviously occur in the z axis. These are principal stresses and their expression is
B.3. CONCLUSION
109
given by [77]
σ1 = σ2


1
1
z
(1 + ν) − = −Pmax  1 − tan−1 z
2 
a
a
2 1 + az
σ3 =
−Pmax
2 .
1 + az
(B.22)
The corresponding shearing stress are given by
σ1 − σ2
=0
2
σ2 − σ3
σ1 − σ3
=
.
=
2
2
τxy =
τxz = τyz
(B.23)
With these expressions, the curve representing the stresses per unit of Pmax
versus the depth in the z axis per unit of radius of contact area a can be
drawn (Fig.B.4).
Figure B.4: Principal, von Mises and shearing contact stress
Fig.B.4 shows that the maximal von Mises stress occur just below the surface,
at a depth of 0.5a, and with an amplitude of
max
σef
f = 0.6Pmax .
(B.24)
110
APPENDIX B. CONTACT PRESSURE AND STRESSES
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Curriculum Vitae
Name
Date of birth
Nationality
Marital status
DENIS CROTTET
12th August 1976, Fribourg, Switzerland
Swiss
Married
EDUCATION
2001-2005
Ph.D. in Biomedical Engineering & Microtechnique
Laboratoire de Systèmes Robotiques, EPF Lausanne
1996-2001
M.Sc. in Physics
Department of Physics, EPF Lausanne
1992-1996
High school, scientific section
Collège Sainte-Croix, Fribourg
PROFESSIONNAL EXPERIENCES/PROJECTS
2001-2005
MEM Research Center for Orthopaedic Surgery, Bern
"A FORCE-SENSING DEVICE FOR TKA": Development of a
force-sensing device to help the surgeon balance soft-tissues during
total knee arthroplasty.
2000-2001
Institut de Physique Expérimentale, EPF Lausanne
"ANTENNAE COMPATIBLE FOR ENDOVASCULAR MRI":
Development of an endovascular antenna able to provide high resolution magnetic resonance images for diagnosis of vascular diseases.
1999-2000
CFG Microelectronics, Morges
Summer internship followed by a part-time work
"ORGANIC LIGHT EMITTING DIODES": Identification of the
lifetime-limiting parameters of organic light emitting diodes.
119
120
JOURNAL ARTICLES
1. Crottet D., Kowal J., Sarfert S.A., Maeder T., Bleuler H., Nolte L.P.,
Dürselen L., Ligament Balancing in TKA: Evaluation of a Force-Sensing
Device and the Influence of Patellar Eversion and Ligament Release,
Journal of Biomechanics, submitted
2. Crottet D., Maeder T., Fritschy D., Bleuler H., Nolte L.P., Pappas
I.P., Development of a Force Amplitude- and Location-Sensing Device
Designed to Improve the Ligament Balancing Procedure in TKA, IEEE
Transactions on Biomedical Engineering, vol. 52(9), pp. 1609-1611,
September 2005
3. Crottet D., Meuli R., Wicky S., van der Klink J.J., Reciprocity and
Sensitivity of Opposed-Solenoid Endovascular MRI Probes, Journal of
Magnetic Resonance, vol. 159, pp. 219-225, December 2002
CONFERENCE ABSTRACTS
1. Crottet D., Kowal J., Sarfert S.A., Bleuler H., Nolte L.P., Dürselen
L., In-Situ Evaluation of a Force-Measuring Device for Assistance in
Ligament Balancing during Knee Arthroplasty, 5th Annual Meeting of
the International Society for Computer Aided Orthopaedic Surgery,
147-8, Helsinki, Finland, June 2005
2. Crottet D., Maeder T., Sarfert S., Fritschy D., Bleuler H., Nolte L.P.,
Pappas I.P., In-vitro Evaluation of a Force-Sensing Device for Ligament
Balancing in TKA, 51st Annual Meeting of the Orthopaedic Research
Society, Washington, USA, February 2005
3. Crottet D., Maeder T., Fritschy D., Bleuler H., Nolte L.P., Pappas
I.P., In-vitro Validation of a Device Measuring the Tibio-femoral Contact Forces and Moments for Assistance during Ligament Balancing in
TKA, 17th Annual Symposium of the International Society for Technology in Arthroplasty, Rome, Italy, September 2004
4. Crottet D., Maeder T., Fritschy D., Bleuler H., Nolte L.P., Pappas I.P.,
A Force-Sensing Device for Ligament Balancing in Total Knee Arthroplasty, 4th Annual Meeting of the International Society for Computer
Aided Orthopaedic Surgery, 147-8, Chicago, USA, June 2004
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PATENT
1. D. Crottet, I.P. Pappas, T. Maeder, C. Jacq, H. Bleuler, Device for
Measuring Tibio-Femoral Force Amplitudes and Force Locations in Total Knee Arthroplasty, international patent application, PCT/CH04/
000361, June 2004.
AWARDS
1. 2005 Research Award of the Swiss Society of Biomedical Engineering
2. 2004 Best Poster Award of the 4th Annual Meeting of the International
Society for Computer Aided Orthopaedic Surgery